Question

The center of a circle of a circle is at Q(0,6), a radius is drawn from Q to P(4,6). what are the coordinates of the endpoint of the diameter that includes segment PQ?

A. (0,2)

b. (0,10)

c. (-4,6)

d. (6,-4)

Answer 1

(-4,6) or C

Explanation:

Givens

• x_center = 0
• y_center = 6
• x_center = (x1 + x2)/2
• y_center = (y1 + y2)/2
• x1 = 4
• y1 = 6
• Solve for x2 and y2

Solution

• x_center = (4 + x2) / 2 = 0 Multiply both sides by 2
• 0*2 = (4 + x2)*2 Divide by 2
• 0 = 4 + x2 Subtract 4 from both sides.
• -4 = x2
• You can now declare an answer. The answer must be C

Discussion

• A and B both have an x value of 0. Not correct.
• D is backwards.
• Just to make sure, we'll solve for y2
• y_center = 6
• 6 = (y1 + y2)/2 Multiply by 2
• 6*2 = y1 + y2 Comgine
• 12 = 6 + y2 Subtract 6 from both sides
• 12-6 = y2
• y2 = 6
• Which is just what C says.