Question 1

Given the points $$A(2, 3)$$ and $$B(6, 11)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(6-2)^2$ + (11-3)^2$} = \sqrt{16 + 64} = \sqrt{80}$$

Question 2

What is the midpoint of the segment connecting the points $$(-4, 7)$$ and $$(2, -1)$$?

Accepted Answer

$$\left(\frac{-4+2}{2}, \frac{7+(-1)}{2}\right) = (-1, 3)$$

Question 3

Which of the following lines is perpendicular to the line $$y = 2x + 5$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 4

Find the equation of the line passing through $$(1, -2)$$ with slope $$m = 4.$$

Accepted Answer

$$y + 2 = 4(x - 1)$$

Question 5

A circle has center $$(3, -2)$$ and radius $$5. $$What is its equation?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 6

Which of the following is the general form of the equation of a circle?

Accepted Answer

$$x^2$$ + $$y^2 + Dx + Ey + F = 0$

Question 7

Given the line $$y = -\frac{3}{4}x + 2$$, what is the slope of a line parallel to it?

Accepted Answer

$$-\frac{3}{4}$$

Question 8

If the product of the slopes of two lines is $$-1$$, what can be said about the lines?

Accepted Answer

The lines are perpendicular.

Question 9

Find the $$x-$$intercept of the line $$2x - 3y = 6.$$

Accepted Answer

$$x = 3$$

Question 10

A vertical line passes through the point $$(5, -1). $$What is its equation?

Accepted Answer

$$x = 5$$

Question 11

Given the equation $$y = 3x - 7$$, what is the $$y-$$intercept?

Accepted Answer

$$-7$$

Question 12

Which of the following points lies on the circle $$(x - 2)^2$ + (y + 1)^2$ = 9$$?

Accepted Answer

$$(5, -1)$$

Question 13

Find the equation of the line perpendicular to $$y = -2x + 4$$ and passing through $$(0, 3).$$

Accepted Answer

$$y - 3 = \frac{1}{2}x$$

Question 14

A chemical reaction requires a temperature to increase at a constant rate. If the temperature starts at $$20^\circC $$and increases by $$3^\circC $$per minute, which equation models the temperature $$T$$ after $$t$$ minutes?

Accepted Answer

$$T = 3t + 20$$

Question 15

A circle has the equation $$x^2$$ + $$y^2 - 4x + 6y = 12$. What is the center and radius of the circle?

Accepted Answer

Center $$(2, -3)$$, radius $$5$$

Question 16

Which of the following is the point-slope form of the equation of a line?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 17

A medical researcher tracks the growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, which equation best models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = P_0$ \cdot 2^t$$

Question 18

Find the slope of the line passing through the points $$(1, 2)$$ and $$(4, 8).$$

Accepted Answer

$$m = \frac{8 - 2}{4 - 1} = 2$$

Question 19

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = c$$

Lines and Circles: Formulas, Equations, and Applications in Precalculus

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