How do you find the center of a circle given the endpoints of a diameter?

The center is found by averaging the x-coordinates and y-coordinates of the endpoints: $$igg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} igg)$$ .

What is the formula for the radius of a circle given its diameter?

The radius is half the length of the diameter: $$r = \frac{d}{2}$$ .

How do you derive the equation of a circle from its center and radius?

The equation of a circle with center (h,k) and radius r is: $$(x - h)^2 + (y - k)^2 = r^2$$ .

What is the significance of the distance formula in coordinate geometry?

The distance formula allows us to calculate the straight-line distance between two points in a coordinate plane.

What does the midpoint of a segment represent?

The midpoint of a segment is the point that divides the segment into two equal parts.

How can you determine if two points are the same using the distance formula?

If the distance between two points is zero, then the points are the same: $$d = 0 \text{ implies } (x_1, y_1) = (x_2, y_2)$$ .

What is the relationship between the endpoints of a diameter and the center of a circle?

The center of a circle is the midpoint of the diameter.

How do you find the coordinates of a point given its distance from another point?

Use the distance formula to set up an equation and solve for the unknown coordinates.

Unit 4 Practice Test Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Find the distance between the points (2,-6) and (-4,8).

Back

2.

FLASHCARD QUESTION

Front

Given the distance = 5 units between (2,-1) and (x,-5). Find the values of x.

Back

3.

FLASHCARD QUESTION

Front

Find the midpoint between (4,-6) and (-8,10).

Back

4.

FLASHCARD QUESTION

Front

Given the endpoints of a segment are (x+3, 6-y) and (4, 2y) with midpoint (-2,6). Find the value of x.

Back

5.

FLASHCARD QUESTION

Front

Write the equation in center-radius form for the diameter endpoints (-12,-6) and (2,-4).

Back

6.

FLASHCARD QUESTION

Front

What is the distance formula?

Back

7.

FLASHCARD QUESTION

Front

What is the midpoint formula?

Back

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