Question 1

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 $d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to the given points $P(3\sqrt{5}, 5\sqrt{7})$ and $Q(-2\sqrt{5}, -9\sqrt{7})$, we get $d(P, Q) = \sqrt{((-2\sqrt{5} - 3\sqrt{5})^2 + (-9\sqrt{7} - 5\sqrt{7})^2)} = \sqrt{(5\sqrt{5})^2 + (14\sqrt{7})^2} = \sqrt{125 + 1372} = \sqrt{1497}$.

Question 2

Determine whether the three points are the vertices of a right triangle.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

To determine if the points form a right triangle, calculate the distances between each pair of points and check if the Pythagorean theorem holds. The distances are:  1. Between (-6,7) and (5,-4): √((5+6)² + (-4-7)²) = √(11² + (-11)²) = √(121 + 121) = √242  2. Between (5,-4) and (7,-2): √((7-5)² + (-2+4)²) = √(2² + 2²) = √8  3. Between (-6,7) and (7,-2): √((7+6)² + (-2-7)²) = √(13² + (-9)²) = √(169 + 81) = √250  Check if any combination satisfies the Pythagorean theorem:  √242 + √8 = √250  Since the sum of the squares of the two shorter sides equals the square of the longest side, the points form a right triangle.

Question 3

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 $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. For $P(13\sqrt{3}, \sqrt{10})$ and $Q(-\sqrt{3}, 4\sqrt{10})$, the midpoint is $\left( \frac{13\sqrt{3} - \sqrt{3}}{2}, \frac{\sqrt{10} + 4\sqrt{10}}{2} \right) = \left( 6\sqrt{3}, \frac{5\sqrt{10}}{2} \right)$.

Question 4

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(7, -9) and Q(0, 8) gives $\left( \frac{7 + 0}{2}, \frac{-9 + 8}{2} \right) = \left( \frac{7}{2}, -\frac{1}{2} \right)$.

Question 5

For the points P and Q, find the coordinates of the midpoint of the segment PQ.&#10;P(5, 9), Q(7, 1)

Accepted Answer

The midpoint of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. For P(5, 9) and Q(7, 1), the midpoint is $\left(\frac{5 + 7}{2}, \frac{9 + 1}{2}\right) = (6, 5)$.

Question 6

Determine whether the three points are the vertices of a right triangle.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

The distance between (-2,3) and (0,7) is 5. The distance between (0,7) and (2,6) is 1. The distance between (-2,3) and (2,6) is 5. 5^2 = 1^2 + 5^2, so the triangle is 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 $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For points P(-2, -3) and Q(1, 6), the distance is $\sqrt{(1 - (-2))^2 + (6 - (-3))^2} = \sqrt{3^2 + 9^2} = \sqrt{9 + 81} = \sqrt{90} = 3\sqrt{10}$.

Question 8

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(7, -2) and Q(5, 2), we get $d = \sqrt{(5 - 7)^2 + (2 - (-2))^2} = \sqrt{(-2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5}$.

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 $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this to points P(3, -5) and Q(7, -7), we get $\sqrt{(7 - 3)^2 + (-7 + 5)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$.

Question 10

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(0, -1) and Q(8, 8) gives $\left( \frac{0 + 8}{2}, \frac{-1 + 8}{2} \right) = \left( 4, \frac{7}{2} \right)$.

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

Determine whether the three points are the vertices of a right triangle.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 14

Determine whether the three points are the vertices of a right triangle.&#10; &#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; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 16

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 17

List the ordered pairs from the table.&#10; &#10;A) (3, 1), (0, 2), (-6, 4), (-9, 5)&#10;B) (1, 0), (2, 3), (4, -9), (5, -6)&#10;C) (1, -9), (2, -6), (4, 0), (5, 3)&#10;D) (1, 3), (2, 0), (4, -6), (5, -9)

Accepted Answer

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

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

List the ordered pairs from the table.&#10;Sales at the University Bookstore  &#10;A) (1, 180,000), (2, 720,000), (3, 300,000), (4, 1,060,000)&#10;B) (720,000, 1), (180,000, 2), (1,060,000, 3), (300,000, 4)&#10;C) (1, 720,000), (2, 180,000), (3, 1,060,000), (4, 300,000)&#10;D) (300,000, 1), (1,060,000, 2), (180,000, 3), (720,000, 4)

Accepted Answer

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

Question 20

Determine whether the three points are the vertices of a right triangle.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 21

Determine whether the three points are collinear.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 22

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 23

Determine whether the three points are collinear.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 24

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 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;

Accepted Answer

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

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

Determine whether the three points are collinear.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 29

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
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.
Average Monthly Payment to Retirees

A) $36
B) $524
C) $488
D) $500

Accepted Answer

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

Question 30

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 31

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 32

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 33

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
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.
Average Monthly Payment to Retirees

A) $36
B) $524
C) $488
D) $500

Accepted Answer

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

Question 34

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.&#10;midpoint (-8, 7), endpoint (-4, 6)&#10;A) (-2, -2)&#10;B) (4, 4)&#10;C) (-12, 5)&#10;D) (-12, 8)

Accepted Answer

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

Question 35

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 36

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 37

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
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.
Average Monthly Payment to Retirees

A) $36
B) $524
C) $488
D) $500

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 (c, y), endpoint (m, q)

Accepted Answer

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

Question 39

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 40

Determine whether the three points are collinear.&#10; &#10;A) Yes&#10;B) No

Accepted Answer

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

Question 41

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

Accepted Answer

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

Question 42

Graph the equation by plotting points.&#10;

Accepted Answer

The answer of Graph the equation by plotting points.&#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;If the point (a, b) is in the fourth quadrant, in what quadrant is (b, a)?&#10;A) III&#10;B) IV&#10;C) I&#10;D) II

Accepted Answer

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

Question 45

Find the center-radius form of the equation of the circle.&#10;center (10, 0), radius 3

Accepted Answer

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

Question 46

Provide an appropriate response.&#10;What is the distance from the point (a, w) to the point (m, q)?

Accepted Answer

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

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;If a vertical line is drawn through the point (3, -4), where will it intersect the x-axis?&#10;A) (0, -4)&#10;B) (3, 0)&#10;C) (0, 3)&#10;D) (-4, 0)

Accepted Answer

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

Question 50

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 51

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 52

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

Accepted Answer

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

Question 53

Provide an appropriate response.&#10;

Accepted Answer

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

Question 54

Provide an appropriate response.&#10;Are the points A(-3, 5), B(0, 6), C(2, -2), and D(5, 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) yes; no&#10;C) yes; yes&#10;D) no; yes

Accepted Answer

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

Question 55

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 56

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 57

Find the center-radius form of the equation of the circle.&#10;center (0, 2), radius 4

Accepted Answer

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

Question 58

Graph the equation by plotting points.&#10;

Accepted Answer

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

Question 59

Provide an appropriate response.&#10;

Accepted Answer

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

Question 60

Provide an appropriate response.&#10;Are the points A(3, 6), B(6, 9), C( 8, 1), and D(11, 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) yes; no&#10;C) no; yes&#10;D) no; no