Question 1

Which of the following best describes the origin in the Cartesian coordinate plane?

Accepted Answer

The point where the x-axis and y-axis intersect, represented by $$(0,0).$$

Question 2

Given the point $$(-4,2)$$, in which quadrant of the Cartesian plane does it lie?

Accepted Answer

Quadrant II

Question 3

Which ordered pair is a solution to the equation $$y = -4x + 10$$?

Accepted Answer

$$(1.5, 8)$$

Question 4

What is the distance between the points $$(3,4)$$ and $$(-2,2)$$?

Accepted Answer

$$\sqrt{29}$$

Question 5

Which formula is used to find the midpoint between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 6

If a circle has the equation $$(x-3)^2$$ + $$(y-8)^2 = 64$, what is the center and radius of the circle?

Accepted Answer

Center: $$(3,8)$$, Radius: $$8$$

Question 7

Which of the following points is NOT located in Quadrant III?

Accepted Answer

$$(2,-4)$$

Question 8

A city plans to build a circular park with center at $$(2, -1)$$ and radius $$5. $$What is the equation of the park's boundary?

Accepted Answer

$$(x-2)^2$$ + $$(y+1)^2 = 25$

Question 9

Which statement about the axes in the Cartesian plane is correct?

Accepted Answer

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

Question 10

Given the equation $$5x + 2y = 70$$, which ordered pair is a solution?

Accepted Answer

$$(12,5)$$

Question 11

A drone flies from point $$A(2,3) to $$point $$B(6,4). $$What is the midpoint of its path?

Accepted Answer

$$(4, 3.5)$$

Question 12

Which of the following is the correct method to find the x-intercept of a linear equation?

Accepted Answer

Set $$y = 0$$ and solve for $$x.$$

Question 13

A biologist tracks two animals at $$(2,3)$$ and $$(6,4). $$What is the distance between them?

Accepted Answer

$$\sqrt{17}$$

Question 14

Which of the following points is in Quadrant IV?

Accepted Answer

$$(4,-5)$$

Question 15

A circle has center $$(-1,-1)$$ and radius $$7. $$What is its equation in standard form?

Accepted Answer

$$(x+1)^2$$ + $$(y+1)^2 = 49$

Question 16

Which ordered pair represents a point on the y-axis?

Accepted Answer

$$(0,3)$$

Question 17

A company wants to place a sign at the midpoint between its two stores at $$(-4,2)$$ and $$(2,15). $$Where should the sign be placed?

Accepted Answer

$$(-1, 8.5)$$

Question 18

Which of the following is the correct formula for 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 19

Which of the following ordered pairs is NOT a solution to $$y = -4x + 10$$?

Accepted Answer

$$(1,6)$$

Fundamentals of the Cartesian Plane and Coordinate Geometry

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