Question 1

What is the distance between the points $$A(2, -3)$$ and $$B(-4, 5)$$? Express your answer in simplified radical form.

Accepted Answer

$$\sqrt{100}$$

Question 2

Which formula correctly gives the distance $$d$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the coordinate plane?

Accepted Answer

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

Question 3

Find the midpoint of the line segment with endpoints $$(6, -2)$$ and $$(-2, 8).$$

Accepted Answer

$$(2, 3)$$

Question 4

Which formula gives the midpoint $$M of a $$segment with endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Given the equation of a circle $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$, what is the center and radius of the circle?

Accepted Answer

Center $$(3, -4)$$, radius $$2$$

Question 7

Which of the following best describes a circle in the coordinate plane?

Accepted Answer

The set of all points equidistant from a fixed point called the center.

Question 8

Convert the general form $$x^2$$ + $$y^2 + 4x - 6y - 12 = 0$ to standard form.

Accepted Answer

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

Question 9

A circular fountain in a park has its center at $$(0, 0)$$ and a radius of $$7$$ meters. Which equation models the edge of the fountain?

Accepted Answer

$$x^2$$ + $$y^2 = 49$

Question 10

If the endpoints of a diameter of a circle are $$(-2, 5)$$ and $$(6, -3)$$, what is the equation of the circle?

Accepted Answer

$$(x - 2)^2$ + (y - 1)^2$ = 32$$

Question 11

A circle has the equation $$(x - 1)^2$ + (y + 2)^2$ = 36. $$What are the coordinates of its center and its radius?

Accepted Answer

Center $$(1, -2)$$, radius $$6$$

Question 12

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

Accepted Answer

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

Question 13

A city plans to build a circular walking path with center at $$(4, -1)$$ and passing through the point $$(7, 3). $$What is the equation of the path?

Accepted Answer

$$(x - 4)^2$ + (y + 1)^2$ = 25$$

Question 14

Which of the following best describes the radius of a circle?

Accepted Answer

The fixed distance from the center to any point on the circle.

Question 15

Given the circle $$x^2$$ + $$y^2 + 2x - 4y - 4 = 0$, what is the center and radius?

Accepted Answer

Center $$(-1, 2)$$, radius $$3$$

Distance and Midpoint Formulas; Circles – Study Notes

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