Question 1

Given the points $$P(-5, -6)$$ and $$Q(7, -1)$$, what is the distance $$d(P, Q)$$ between them?

Accepted Answer

$$\sqrt{(7 - (-5))^2$ + ((-1) - (-6))^2$} = \sqrt{12^2$ + 5^2$} = \sqrt{144 + 25} = \sqrt{169} = 13$$

Question 2

What are the coordinates of the midpoint $$M of $$the segment with endpoints $$P(8, 2)$$ and $$Q(3, 5)$$?

Accepted Answer

$$\left( \frac{8 + 3}{2}, \frac{2 + 5}{2} \right) = (5.5, 3.5)$$

Question 3

Which quadrant does the point $$(-4, 3)$$ lie in?

Accepted Answer

Quadrant II

Question 4

If three points $$A$$, $$B$$, and $$C$$ are collinear, which of the following must be true?

Accepted Answer

The sum of the distances between two pairs of points equals the distance between the remaining pair.

Question 5

Given the equation $$y = \frac{1}{2}x - 2$$, which of the following is an ordered pair solution?

Accepted Answer

$$(4, 0)$$

Question 6

What is the $$y-$$intercept of the equation $$3x - 2y = 6$$?

Accepted Answer

$$(0, -3)$$

Question 7

Which of the following best describes the process of graphing an equation by point plotting?

Accepted Answer

Find intercepts, find additional ordered pairs, plot the points, and join them with a smooth line or curve.

Question 8

Given $$P(-8, 4)$$ and $$Q(3, -5)$$, what is the distance $$d(P, Q)$$?

Accepted Answer

$$\sqrt{(3 - (-8))^2$ + ((-5) - 4)^2$} = \sqrt{11^2$ + (-9)^2$} = \sqrt{121 + 81} = \sqrt{202}$$

Question 9

Which of the following is the correct formula for the midpoint $$M of a $$segment with endpoints $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 10

For the equation $$y = |x - 2|$$, which of the following is NOT a solution?

Accepted Answer

$$(1, 2)$$

Question 11

A chemist plots the temperature and pressure of a gas sample on a rectangular coordinate system. If the ordered pair $$(a, b)$$ represents a measurement, what does $$a$$ and $$b$$ represent?

Accepted Answer

$$a is $$the temperature and $$b is $$the pressure.

Question 12

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 3$$

Question 13

If the distance between $$P(2, 3)$$ and $$Q(x, 5) is$$ $$5$$, what is a possible value of $$x$$?

Accepted Answer

$$x = 6$$

Question 14

Which of the following is the correct distance formula between two points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 15

Which of the following points lies in Quadrant IV?

Accepted Answer

$$(5, -2)$$

Question 16

If the midpoint of $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$) is$$ $$(0, 0)$$, and $$P is$$ $$(4, -6)$$, what are the coordinates of $$Q$$?

Accepted Answer

$$(-4, 6)$$

Study Guide: Distance, Midpoint, and Graphing Equations in College Algebra

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