Question 1

Which of the following points lies in Quadrant II of the Cartesian coordinate system?

Accepted Answer

(−2, 4)

Question 2

Given the equation $$2x + 3y = 18$$, which of the following ordered pairs is a solution?

Accepted Answer

$$(2, 5)$$

Question 3

What is the y-intercept of the line $$2x + 3y = 18$$?

Accepted Answer

$$(0, 6)$$

Question 4

A medical researcher plots the locations of two clinics at $$(−2, 2)$$ and $$(3, −6) on a $$city map. What is the distance between the clinics?

Accepted Answer

$$\sqrt{89}$$

Question 5

A delivery drone must fly from $$(−1, −5) to$$ $$(−1, 2). $$What is the distance it must travel?

Accepted Answer

$$7$$

Question 6

What is the midpoint of the segment connecting $$(−4, −2)$$ and $$(2, 5)$$?

Accepted Answer

$$(−1, \frac{3}{2})$$

Question 7

Which formula correctly represents the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 8

A circular park has its center at $$(3, −7)$$ and a radius of $$5$$ units. What is the equation of the park's boundary?

Accepted Answer

$$(x − 3)^2$ + (y + 7)^2$ = 25$$

Question 9

Which of the following is the standard form equation for a circle centered at the origin with radius $$r$$?

Accepted Answer

$$x^2$$ + $$y^2$$ = $$r^2$$

Question 10

A circle has the equation $$(x − 2)^2$ + (y + 1)^2$ = 16. $$What are its center and radius?

Accepted Answer

Center $$(2, −1)$$, radius $$4$$

Question 11

A biologist wants to find the midpoint between two research stations at $$(−3, 7)$$ and $$(5, −1). $$What are the coordinates of the midpoint?

Accepted Answer

$$(1, 3)$$

Question 12

Which of the following statements about the Cartesian coordinate system is TRUE?

Accepted Answer

The x-axis is the horizontal axis and the y-axis is the vertical axis.

Question 13

If a circle has the equation $$x^2$$ + $$y^2 = 49$, what is the radius?

Accepted Answer

$$7$$

Question 14

A line passes through the points $$(1, 2)$$ and $$(4, 8). $$What is the distance between these points?

Accepted Answer

$$\sqrt{(4 − 1)^2$ + (8 − 2)^2$} = \sqrt{9 + 36} = \sqrt{45}$$

Question 15

A circle is centered at $$(−5, 2)$$ and passes through the point $$(−5, 7). $$What is the equation of the circle?

Accepted Answer

$$(x + 5)^2$ + (y − 2)^2$ = 25$$

Question 16

Which of the following is NOT a solution to the equation $$x + y = 5$$?

Accepted Answer

$$(4, 4)$$

Question 17

A circle has the equation $$(x − h)^2$ + (y − k)^2$ = r^2$. Which statement is correct?

Accepted Answer

The center is $$(h, k)$$ and the radius is $$r.$$

Question 18

A city planner wants to place a fountain exactly halfway between two intersections at $$(6, 2)$$ and $$(−2, 8). $$What are the coordinates of the fountain?

Accepted Answer

$$(2, 5)$$

Question 19

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

Accepted Answer

A point where $$y = 0$$

Question 20

A circle has the equation $$(x − 4)^2$ + (y + 3)^2$ = 36. $$What is the radius?

Accepted Answer

$$6$$

Introduction to Graphing: Cartesian Coordinates, Distance, Midpoint, and Circles

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