Question 1

Which quadrant does the point $$(-4, 7)$$ lie in on the Cartesian coordinate system?

Accepted Answer

Quadrant II

Question 2

Given the equation $$2x + 3y = 18$$, what is the x-intercept of the graph?

Accepted Answer

$$(9, 0)$$

Question 3

Which of the following ordered pairs is a solution to the equation $$2x + 3y = 18$$?

Accepted Answer

$$(3, 4)$$

Question 4

What is the distance between the points $$(-2, 2)$$ and $$(3, -6)$$?

Accepted Answer

$$\sqrt{89}$$

Question 5

Find the midpoint of the segment with endpoints $$(4, -2)$$ and $$(2, 5).$$

Accepted Answer

$$(3, 1.5)$$

Question 6

Which equation represents a circle with center $$(3, -7)$$ and radius $$5$$?

Accepted Answer

$$(x-3)^2$$ + $$(y+7)^2 = 25$

Question 7

Given the equation of a circle $$(x-2)^2$$ + $$(y+4)^2 = 49$, what is the center and radius?

Accepted Answer

Center $$(2, -4)$$, radius $$7$$

Question 8

A biologist tracks the movement of a tagged animal from $$(1, 2) to$$ $$(7, 8). $$What is the total distance traveled?

Accepted Answer

$$\sqrt{72}$$

Question 9

Which of the following is the correct formula for the midpoint between $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 10

A chemical reaction is modeled by the equation $$4x + 2y = 20. $$What is the y-intercept?

Accepted Answer

$$(0, 10)$$

Question 11

Which of the following best describes the graph of the equation $$x^2$$ + $$y^2$$ = $$r^2$$?

Accepted Answer

A circle centered at $$(0, 0)$$ with radius $$r$$

Question 12

A city planner wants to place a fountain equidistant from the corners $$(0, 0)$$ and $$(6, 8). $$What are the coordinates of the fountain?

Accepted Answer

$$(3, 4)$$

Question 13

If the equation of a circle is $$(x+2)^2$$ + $$(y-5)^2 = 36$, what is the radius?

Accepted Answer

$$6$$

Question 14

Which of the following points is NOT a solution to $$x + y = 10$$?

Accepted Answer

$$(3, 5)$$

Question 15

A medical researcher plots the location of two samples at $$(2, 3)$$ and $$(8, 15). $$What is the midpoint between the samples?

Accepted Answer

$$(5, 9)$$

Question 16

Which of the following is the correct formula for the distance between $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 17

A circle has the equation $$(x-1)^2$$ + $$(y+2)^2 = 16$. What are the coordinates of its center?

Accepted Answer

$$(1, -2)$$

Question 18

Which of the following best describes the y-intercept of a graph?

Accepted Answer

The point where the graph crosses the y-axis

Question 19

A circle is drawn with center at $$(0, 0)$$ and radius $$10. $$Which equation represents this circle?

Accepted Answer

$$x^2$$ + $$y^2 = 100$

Question 20

A student claims that the point $$(0, 0) is $$the x-intercept of the equation $$2x + 3y = 18. Is $$this correct?

Accepted Answer

No, because substituting $$y = 0$$ gives $$x = 9$$

Introduction to Graphing: Cartesian Coordinates, Intercepts, and Circles

Study Guide - Practice Questions