Question

Coordinate Proofs Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 1 of 51 of 5 Items Question The center of circle C is at (6,2) , with a radius of 5. In order to prove that point D(6,−3) lies on the circle, what does the length of segment CD¯¯¯¯¯¯¯¯ need to be?(1 point) Segment CD¯¯¯¯¯¯¯¯ must have a length of . Remaining Attempts : 3 Skip to navigation page 17 of 18

Answer 1

To determine whether point \( D(6, -3) \) lies on circle \( C \) with center \( (6, 2) \) and radius \( 5 \), we need to find the distance \( CD \) between the center of the circle \( C(6, 2) \) and point \( D(6, -3) \).

We can use the distance formula, which is given by:

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

In this case:

- \( (x_1, y_1) = (6, 2) \) (the center of the circle)
- \( (x_2, y_2) = (6, -3) \) (point D)

Substituting the values into the distance formula:

\[
d = \sqrt{(6 - 6)^2 + (-3 - 2)^2}
\]

This simplifies to:

\[
d = \sqrt{(0)^2 + (-5)^2}
\]
\[
d = \sqrt{0 + 25}
\]
\[
d = \sqrt{25}
\]
\[
d = 5
\]

Since the radius of the circle is \( 5 \), and the length of segment \( CD \) is also \( 5 \), point \( D \) indeed lies on the circle.

Therefore, the length of segment \( CD \) must be \( 5 \).