Question 1

Given the points $$A(1,2)$$ and $$B(5,8)$$, what is the distance between them?

Accepted Answer

$$\sqrt{52}$$

Question 2

What is the midpoint between the points $$(1,2)$$ and $$(5,8)$$?

Accepted Answer

$$(3,5)$$

Question 3

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

Accepted Answer

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

Question 4

A circle has the equation $$(x-2)^2$$ + $$(y+3)^2 = 25$. What are the center and radius of the circle?

Accepted Answer

Center: $$(2, -3)$$, Radius: $$5$$

Question 5

Which equation represents a circle with center at $$(-4, 2)$$ and radius $$7$$?

Accepted Answer

$$(x+4)^2$$ + $$(y-2)^2 = 49$

Question 6

Given the equation $$x^2 + 4x$$ + $$y^2 = 8$, what is the center and radius of the circle after completing the square?

Accepted Answer

Center: $$(-2, 0)$$, Radius: $$2\sqrt{3}$$

Question 7

A city plans to build a circular park with its center at $$(3, -4)$$ and a radius of $$7$$ units. Which equation models the boundary of the park?

Accepted Answer

$$(x-3)^2$$ + $$(y+4)^2 = 49$

Question 8

If the endpoints of a diameter of a circle are $$(2, 5)$$ and $$(8, 11)$$, what is the equation of the circle?

Accepted Answer

$$(x-5)^2$$ + $$(y-8)^2 = 18$

Question 9

Which of the following best describes the geometric meaning of the distance formula?

Accepted Answer

It gives the length of the straight line segment connecting two points in the plane.

Question 10

A drone flies from point $$A(2,3) to $$point $$B(10,15). $$What is the straight-line distance it travels?

Accepted Answer

$$14$$

Question 11

Given the equation $$x^2 - 6x$$ + $$y^2 + 8y = 3$, what is the center and radius of the circle?

Accepted Answer

Center: $$(3, -4)$$, Radius: $$\sqrt{7}$$

Question 12

A cell phone tower is located at $$(0,0). If $$its signal reaches up to $$10$$ units away, what is the equation of the boundary of its coverage area?

Accepted Answer

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

Question 13

If a circle has the equation $$(x+1)^2$$ + $$(y-7)^2 = 81$, what is the center and radius?

Accepted Answer

Center: $$(-1, 7)$$, Radius: $$9$$

Question 14

A rectangular garden has its corners at $$(1,2)$$ and $$(5,8). $$What is the length of the diagonal of the garden?

Accepted Answer

$$\sqrt{52}$$

Question 15

Which of the following is the standard form of the equation of a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x-h)^2$$ + $$(y-k)^2$$ = $$r^2$$

Question 16

A hospital is located at $$(4, -3). If $$its emergency response radius is $$6$$ units, which equation represents the area it can reach?

Accepted Answer

$$(x-4)^2$$ + $$(y+3)^2 = 36$

Question 17

If the midpoint between two points is $$(7, -2)$$ and one endpoint is $$(3, 4)$$, what is the other endpoint?

Accepted Answer

$$(11, -8)$$

Question 18

A circle passes through the points $$(0,0)$$ and $$(6,0)$$ and has its center on the $$x-$$axis. What is the equation of the circle?

Accepted Answer

$$(x-3)^2$$ + $$y^2 = 9$

Coordinate Geometry: Points, Distance, Midpoint, and Circles

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