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 $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. For points P(-8, -5) and Q(-2, -1), the midpoint is $\left( \frac{-8 + (-2)}{2}, \frac{-5 + (-1)}{2} \right) = (-5, -3)$.

Question 2

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

Accepted Answer

The correct ordered pairs, directly taken from the table, are $(-5, -7)$, $(-4, -5)$, $(-2, -1)$, and $(-1, 1)$, which matches choice C.

Question 3

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 $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to points P(-5, -1) and Q(7, -4), we get $d = \sqrt{(7 - (-5))^2 + (-4 - (-1))^2} = \sqrt{(12)^2 + (-3)^2} = \sqrt{144 + 9} = \sqrt{153} = 3\sqrt{17}$.

Question 4

Determine whether the three points are the vertices of a right triangle.&#10;(9, 6), (15, 8), (14, 3)&#10;A) Yes&#10;B) No

Accepted Answer

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

Question 5

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

Accepted Answer

The ordered pairs should list the month first, followed by the sales for that month, as shown in the table.

Question 6

Determine whether the three points are the vertices of a right triangle.&#10;(-7, 4), (-1, 6), (3, -6)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points form a right triangle, we can use the distance formula to calculate the lengths of the sides and then check if the Pythagorean theorem holds for any two sides and the hypotenuse. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.1. Distance between (-7, 4) and (-1, 6): $\sqrt{(-1+7)^2 + (6-4)^2} = \sqrt{36 + 4} = \sqrt{40}$2. Distance between (-1, 6) and (3, -6): $\sqrt{(3+1)^2 + (-6-6)^2} = \sqrt{16 + 144} = \sqrt{160}$3. Distance between (3, -6) and (-7, 4): $\sqrt{(-7-3)^2 + (4+6)^2} = \sqrt{100 + 100} = \sqrt{200}$The lengths are $\sqrt{40}$, $\sqrt{160}$, and $\sqrt{200}$. If we square these, we get 40, 160, and 200. Notice that $40 + 160 = 200$, which satisfies the Pythagorean theorem ($a^2 + b^2 = c^2$). Therefore, the points form a right triangle.

Question 7

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(5,6) and Q(-1,3), we get $\sqrt{(-1 - 5)^2 + (3 - 6)^2} = \sqrt{(-6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45} = 3\sqrt{5}$.

Question 8

Determine whether the three points are the vertices of a right triangle.&#10;(5, 6), (7, 10), (9, 9)&#10;A) Yes&#10;B) No

Accepted Answer

To determine if the three points form a right triangle, we can use the distance formula to calculate the lengths of the sides formed by the points and then apply the Pythagorean theorem. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.1. Distance between (5, 6) and (7, 10): $\sqrt{(7-5)^2 + (10-6)^2} = \sqrt{4 + 16} = \sqrt{20}$2. Distance between (7, 10) and (9, 9): $\sqrt{(9-7)^2 + (9-10)^2} = \sqrt{4 + 1} = \sqrt{5}$3. Distance between (5, 6) and (9, 9): $\sqrt{(9-5)^2 + (9-6)^2} = \sqrt{16 + 9} = \sqrt{25}$The lengths are $\sqrt{20}$, $\sqrt{5}$, and $\sqrt{25}$. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, $\sqrt{25}^2 = \sqrt{20}^2 + \sqrt{5}^2$, or $25 = 20 + 5$, which holds true. Therefore, 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 $(x_2, y_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Substituting the given points P(2,7) and Q(-1,-3), the distance is $\sqrt{(-1-2)^2 + (-3-7)^2} = \sqrt{(-3)^2 + (-10)^2} = \sqrt{9 + 100} = \sqrt{109}$.

Question 10

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 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 coordinates of the midpoint of the segment PQ.&#10;

Accepted Answer

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

Question 14

Determine whether the three points are the vertices of a right triangle.&#10;(-9, 9), (2, -2), (4, 0)&#10;A) Yes&#10;B) No

Accepted Answer

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

Question 15

Determine whether the three points are the vertices of a right triangle.&#10;(-6, -6), (0, -4), (6, -11)&#10;A) Yes&#10;B) No

Accepted Answer

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

Question 16

Determine whether the three points are collinear.&#10;(-2, 6), (6, 4), (-10, 8)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(-2,...

Question 17

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 18

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 19

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 20

Determine whether the three points are the vertices of a right triangle.&#10;(-5, 2), (0, 2), (0, 4)&#10;A) Yes&#10;B) No

Accepted Answer

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

Question 21

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 22

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 23

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 24

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

Accepted Answer

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

Question 25

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 26

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (7, 13), endpoint (10, 9)&#10;A) (18, 3)&#10;B) (16, 1)&#10;C) (4, 5)&#10;D) (4, 17)

Accepted Answer

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

Question 27

Determine whether the three points are collinear.&#10;(-5, -11), (4, 7), (5, 9)&#10;A) Yes&#10;B) No

Accepted Answer

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

Question 28

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 29

Determine whether the three points are collinear.&#10;(0, -12), (-1, -3), (-9, -11)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(0,...

Question 30

Determine whether the three points are collinear.&#10;(7, -3), (-3, 6), (1, 1)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of Determine whether the three points are collinear.&#10;(7,...

Question 31

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
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 Find the coordinates of the other endpoint...

Question 32

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
midpoint (0, 3), endpoint (-4, 8)

A) (4, 13)
B) (4, -2)
C) (-14, 16)
D) (-12, 18)

Accepted Answer

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

Question 33

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 34

Graph the equation by determining the missing values needed to plot the ordered pairs.&#10;    5

Accepted Answer

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

Question 35

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
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 Find the coordinates of the other endpoint...

Question 36

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 37

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (0, 3), endpoint (-4, 8)&#10;A) (4, 13)&#10;B) (4, -2)&#10;C) (-14, 16)&#10;D) (-12, 18)

Accepted Answer

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

Question 38

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (5, 9), endpoint (2, 4)&#10;A) (12, 10)&#10;B) (8, -1)&#10;C) (8, 14)&#10;D) (-4, -6)

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 (0, -5), endpoint (2, -4)&#10;A) (6, -2)&#10;B) (0, -8)&#10;C) (-2, -6)&#10;D) (-2, -3)

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

Provide an appropriate response.&#10;

Accepted Answer

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

Question 43

Provide an appropriate response.&#10;

Accepted Answer

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

Question 44

Provide an appropriate response.&#10;Are the points A(-1, 12), B(2, 9), C(4, 1), and D(7, 4) the vertices of a parallelogram (opposite side 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(-1,...

Question 45

Provide an appropriate response.&#10;What is the midpoint of the segment joining (a, z) and (-5a, 7z)?&#10;A) (2a, 3z)&#10;B) (-3a, 4z)&#10;C) (-2a, 4z)&#10;D) (-4a, 8z)

Accepted Answer

The answer of Provide an appropriate response.&#10;What is the midpoint...

Question 46

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 47

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 48

Provide an appropriate response.&#10;If a vertical line is drawn through the point (-5, 6), where will it intersect the x-axis?&#10;A) (0, 6)&#10;B) (0, -5)&#10;C) (6, 0)&#10;D) (-5, 0)

Accepted Answer

The answer of Provide an appropriate response.&#10;If a vertical line...

Question 49

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 50

Provide an appropriate response.&#10;If the point (a, b) is in the fourth quadrant, in what quadrant is (b, a)?&#10;A) III&#10;B) II&#10;C) I&#10;D) IV

Accepted Answer

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

Question 51

Provide an appropriate response.&#10;If the point (a, b) is in the fourth quadrant, in what quadrant is (-a, -b)?&#10;A) I&#10;B) II&#10;C) III&#10;D) IV

Accepted Answer

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

Question 52

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 53

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 54

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 55

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 56

Provide an appropriate response.&#10;If the point (a, b) is in the fourth quadrant, in what quadrant is (a, -b)?&#10;A) I&#10;B) III&#10;C) IV&#10;D) II

Accepted Answer

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

Question 57

Provide an appropriate response.&#10;If a horizontal line is drawn through the point (5, -2), where will it intersect the y-axis?&#10;A) (0, 5)&#10;B) (-2, 0)&#10;C) (5, 0)&#10;D) (0, -2)

Accepted Answer

The answer of Provide an appropriate response.&#10;If a horizontal line...

Question 58

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 59

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 60

Provide an appropriate response.&#10;Are the points A(1, 6), B(4, 9), C( 6, 1), and D(9, 4) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?&#10;A) yes; yes&#10;B) no; yes&#10;C) no; no&#10;D) yes; no