Question

P is the center of a ˚le with diameter KR.

If P(7, −5) and Q(4, −2), find the coordinates of point K.
a) K(5, −7)
b) K(11, −3)
c) K(1, −9)
d) K(8, −4)

Answer 1

Using the midpoint formula to find the coordinates of point K, considering P as the midpoint and Q as one endpoint of the circle's diameter, results in coordinates (10, -8) for point K. However, this correct pair is not listed in the provided multiple choice options, indicating a potential error in the question or options.

Step-by-step explanation:

To find the coordinates of point K in the given circle with P as the center and KR as the diameter, we need to use the midpoint formula since Q is a point on the circle and K and Q are endpoints of a diameter. Since P is the midpoint of K and Q, we can apply the midpoint formula which is (x1+x2)/2, (y1+y2)/2 where (x1, y1) and (x2, y2) are the coordinates of K and Q, respectively. Since we already have the midpoint P(7, -5) and one endpoint Q(4, -2), we can set up the equations:

(7+x)/2 = 4 and (-5+y)/2 = -2

After solving these equations, we find that the coordinates of K are (10, -8). However, none of the multiple choice options offered for K include this pair of coordinates. It is likely that there is a typo in the question or in the provided options. Hence, we cannot accurately determine which answer is correct based on the given information and choices.