Question 1

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The midpoint formula is $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Applying this to points P(-2, -8) and Q(5, 5) gives $\left( \frac{-2 + 5}{2}, \frac{-8 + 5}{2} \right) = \left( \frac{3}{2}, -\frac{3}{2} \right)$.

Question 2

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The midpoint of a segment with endpoints $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Applying this formula to the given points $P(9\sqrt{7}, \sqrt{11})$ and $Q(-\sqrt{7}, 4\sqrt{11})$, we get the midpoint as $\left( \frac{9\sqrt{7} - \sqrt{7}}{2}, \frac{\sqrt{11} + 4\sqrt{11}}{2} \right) = \left( 4\sqrt{7}, \frac{5\sqrt{11}}{2} \right)$.

Question 3

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The midpoint formula is $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. For points P(2, -6) and Q(0, 2), the midpoint is $(\frac{2+0}{2}, \frac{-6+2}{2}) = (1, -2)$.

Question 4

Determine whether the three points are the vertices of a right triangle.&#10;(9, 1), (15, 3), (14, -2)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are the...

Question 5

Determine whether the three points are the vertices of a right triangle.&#10;

Accepted Answer

The three points form a right triangle because two of the sides are parallel to the x-axis and y-axis, respectively, indicating they meet at a right angle.

Question 6

Determine whether the three points are the vertices of a right triangle.&#10;(-5, 11), (-3, 15), (-1, 14)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points form a right triangle, we can calculate the distances between each pair of points and then check if the Pythagorean theorem holds for any combination of these distances. The distances between the points are as follows:1. Distance between (-5, 11) and (-3, 15): $d_1 = \sqrt{(-3 + 5)^2 + (15 - 11)^2} = \sqrt{4 + 16} = \sqrt{20}$2. Distance between (-3, 15) and (-1, 14): $d_2 = \sqrt{(-1 + 3)^2 + (14 - 15)^2} = \sqrt{4 + 1} = \sqrt{5}$3. Distance between (-5, 11) and (-1, 14): $d_3 = \sqrt{(-1 + 5)^2 + (14 - 11)^2} = \sqrt{16 + 9} = \sqrt{25}$Now, we check if the Pythagorean theorem ($a^2 + b^2 = c^2$) holds for any combination of these distances. It's clear that $d_1^2 + d_2^2 = d_3^2$ because $\sqrt{20}^2 + \sqrt{5}^2 = 20 + 5 = 25 = \sqrt{25}^2$.Therefore, the three points are the vertices of a right triangle.

Question 7

Determine whether the three points are the vertices of a right triangle.&#10;(-13, 13), (-2, 2), (0, 4)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points form a right triangle, we can calculate the distances between each pair of points and then check if the Pythagorean theorem holds for any combination of these distances. The distances between the points are as follows:1. Distance between (-13, 13) and (-2, 2) = sqrt[(-13 + 2)^2 + (13 - 2)^2] = sqrt[121 + 121] = sqrt[242]2. Distance between (-13, 13) and (0, 4) = sqrt[(-13 + 0)^2 + (13 - 4)^2] = sqrt[169 + 81] = sqrt[250]3. Distance between (-2, 2) and (0, 4) = sqrt[(-2 + 0)^2 + (2 - 4)^2] = sqrt[4 + 4] = sqrt[8]If we square these distances, we get 242, 250, and 8. It's clear that 242 + 8 = 250, which means the Pythagorean theorem holds for these distances. Therefore, the three points are the vertices of a right triangle.

Question 8

Determine whether the three points are the vertices of a right triangle.&#10;(6, 4), (12, 6), (16, -6)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points form a right triangle, we can calculate the distances between each pair of points and then check if the Pythagorean theorem holds for any combination of these distances. The distances between the points are as follows:1. Distance between (6, 4) and (12, 6): $\sqrt{(12-6)^2 + (6-4)^2} = \sqrt{6^2 + 2^2} = \sqrt{36 + 4} = \sqrt{40}$2. Distance between (12, 6) and (16, -6): $\sqrt{(16-12)^2 + (-6-6)^2} = \sqrt{4^2 + (-12)^2} = \sqrt{16 + 144} = \sqrt{160}$3. Distance between (6, 4) and (16, -6): $\sqrt{(16-6)^2 + (-6-4)^2} = \sqrt{10^2 + (-10)^2} = \sqrt{100 + 100} = \sqrt{200}$Now, we check if these distances satisfy the Pythagorean theorem ($a^2 + b^2 = c^2$):$\sqrt{40}^2 + \sqrt{160}^2 = \sqrt{200}^2$$40 + 160 = 200$This shows that the distances between the points satisfy the Pythagorean theorem, indicating that the points form a right triangle.

Question 9

For the points P and Q, find the distance d(P, Q).&#10;

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to points P(7, -1) and Q(-5, -7), we get $\sqrt{(-5 - 7)^2 + (-7 + 1)^2} = \sqrt{(-12)^2 + (-6)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$.

Question 10

For the points P and Q, find the distance d(P, Q).&#10;

Accepted Answer

The distance between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ in a plane is given by the formula $d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Substituting the given points $P(3\sqrt{5}, -5\sqrt{11})$ and $Q(4\sqrt{5}, 3\sqrt{11})$ into the formula gives $d(P, Q) = \sqrt{(4\sqrt{5} - 3\sqrt{5})^2 + (3\sqrt{11} + 5\sqrt{11})^2} = \sqrt{(1\sqrt{5})^2 + (8\sqrt{11})^2} = \sqrt{5 + 64 \times 11} = \sqrt{5 + 704} = \sqrt{709}$.

Question 11

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 12

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 13

For the points P and Q, find the distance d(P, Q).&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 14

For the points P and Q, find the distance d(P, Q).&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 15

Determine whether the three points are the vertices of a right triangle.&#10;(10, -8), (16, -6), (22, -13)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are the...

Question 16

List the ordered pairs from the table.&#10;

Accepted Answer

The answer of List the ordered pairs from the table.&#10;...

Question 17

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 18

For the points P and Q, find the distance d(P, Q).&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 19

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

The answer of For the points P and Q, find...

Question 20

List the ordered pairs from the table.&#10;

Accepted Answer

The answer of List the ordered pairs from the table.&#10;...

Question 21

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 22

Determine whether the three points are collinear.&#10;(-4, -9), (0, -1), (6, 11)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(-4,...

Question 23

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (a, w), endpoint (m, q)

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 24

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 25

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (12, -6), endpoint (9, -5)&#10;A) (3, -3)&#10;B) (15, -4)&#10;C) (15, -7)&#10;D) (7, 1)

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 26

Determine whether the three points are collinear.&#10;(-9, 8), (-5, -1), (0, 4)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(-9,...

Question 27

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 28

Solve the problem.&#10;The table shows enrollment in 2-year technical schools for 1980, 1990 and 2000. Assuming a linear relationship, estimate the enrollment for 1995.

Accepted Answer

The answer of Solve the problem.&#10;The table shows enrollment in...

Question 29

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 30

Determine whether the three points are collinear.&#10;(10, 13), (6, 8), (14, 18)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(10,...

Question 31

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 32

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (-6, 0), endpoint (-5, -5)&#10;A) (-7, 5)&#10;B) (5, -7)&#10;C) (-3, -15)&#10;D) (-7, -10)

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 33

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 34

Solve the problem.&#10;The graph shows an idealized linear relationship for the average monthly payment to retirees from 1995 to 1999. Use the midpoint formula to estimate the average payment in 1997.

Accepted Answer

The answer of Solve the problem.&#10;The graph shows an idealized...

Question 35

Solve the problem.&#10;The table lists how financial aid income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the financial aid cutoff for 1985.

Accepted Answer

The answer of Solve the problem.&#10;The table lists how financial...

Question 36

Determine whether the three points are collinear.&#10;(5, -1), (-3, 6), (4, -2)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(5,...

Question 37

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 38

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (-2, -6), endpoint (2, -3)&#10;A) (10, 3)&#10;B) (-4, -11)&#10;C) (-6, -9)&#10;D) (-6, 0)

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 39

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (-2, 0), endpoint (-3, -5)&#10;A) (7, -3)&#10;B) (-1, 5)&#10;C) (-5, -15)&#10;D) (-1, -10)

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 40

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 41

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 42

Find the center-radius form of the equation of the circle.&#10;

Accepted Answer

The answer of Find the center-radius form of the equation...

Question 43

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 44

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 45

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 46

Provide an appropriate response.&#10;If the point (a, b) is in the fourth quadrant, in what quadrant is (a, -b)?

Accepted Answer

The answer of Provide an appropriate response.&#10;If the point (a,...

Question 47

Find the center-radius form of the equation of the circle.&#10;

Accepted Answer

The answer of Find the center-radius form of the equation...

Question 48

Find the center-radius form of the equation of the circle.&#10;

Accepted Answer

The answer of Find the center-radius form of the equation...

Question 49

Provide an appropriate response.&#10;Are the points A(-3, 11), B(0, 8), C(2, 0), and D(5, 3) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?&#10;A) no; yes&#10;B) no; no&#10;C) yes; no&#10;D) yes; yes

Accepted Answer

The answer of Provide an appropriate response.&#10;Are the points A(-3,...

Question 50

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 51

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 52

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 53

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 54

Provide an appropriate response.&#10;If the point (a, b) is in the fourth quadrant, in what quadrant is (-a, -b)?

Accepted Answer

The answer of Provide an appropriate response.&#10;If the point (a,...

Question 55

Find the center-radius form of the equation of the circle.&#10;

Accepted Answer

The answer of Find the center-radius form of the equation...

Question 56

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 57

Provide an appropriate response.&#10;Are the points A(0, 3), B(3, 6), C( 5, -2), and D(8, 1) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?&#10;A) no; no&#10;B) no; yes&#10;C) yes; yes&#10;D) yes; no

Accepted Answer

The answer of Provide an appropriate response.&#10;Are the points A(0,...

Question 58

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 59

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 60

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#10; ...

Question 61

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.&#10; &#10;A) yes&#10;B) no; the graph is nonexistent&#10;C) no; the graph is the point (-5, -3)&#10;D) no; the graph is the point (5, 3)

Accepted Answer

The answer of Decide whether or not the equation has...

Question 62

Find the center-radius form of the equation of the circle.&#10;

Accepted Answer

The answer of Find the center-radius form of the equation...

Question 63

Graph the circle.&#10;

Accepted Answer

The answer of Graph the circle.&#10;   ...

Question 64

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.&#10;

Accepted Answer

The answer of Decide whether or not the equation has...

Deck 2: Graphs and Functions