Question

Find the endpoint MV6. PQ has a midpoint at M(0,6). Point Q is at (0, 3). Find the coordinates of point P. Write the coordinates as decimals or integers.

a) P(0, 0)
b) P(0, 9)
c) P(0, 12)
d) P(0, 5)

Answer 1

The coordinates of point P are found using the midpoint formula. Since M is the midpoint between P and Q, we use M's coordinates (0,6) and Q's coordinates (0,3) to find P's y-coordinate as twice the y of M minus the y of Q, resulting in P(0, 9).

Step-by-step explanation:

The student is seeking to find the coordinates of point P given that M is the midpoint of segment PQ and the coordinates of M and Q are known. The coordinates provided are M(0,6) and Q(0, 3), indicating that we are working in a two-dimensional space on a Cartesian coordinate system. The midpoint M of a line segment is calculated by taking the average of the x-coordinates and y-coordinates of the endpoints P and Q, respectively.

Since M is the midpoint, its x-coordinate and y-coordinate are the averages of the x-coordinates and y-coordinates of P and Q, respectively:
(xM = (xP + xQ)/2, yM = (yP + yQ)/2).
In our case, xM = 0 and yM = 6. The known point Q has coordinates (0, 3) following the same pattern as M for the x-coordinate means the x-coordinate of P will also be 0. Using the midpoint formula in the reverse, you can find the y-coordinate of P:
yP = 2yM - yQ = 2 * 6 - 3 = 12 - 3 = 9.

Therefore, the coordinates for point P are P(0, 9).