Question

The coordinates of the midpoint of the line segment PQ are (1, -2). The coordinates of P are (-3, 2). Find the coordinates of Q.

A) (5, -6)
B) (-5, -2)
C) (-1, -2)
D) (1, 6)

Answer 1

The coordinates of point Q are found by using the midpoint formula to calculate its x and y values based on the midpoint and one endpoint of the segment. By rearranging the midpoint formula and substituting the given values, we can find that the coordinates of Q are (5, -6). The correct option is C.

Step-by-step explanation:

To find the coordinates of point Q given the midpoint coordinates of the line segment PQ and the coordinates of point P, we can use the midpoint formula. The midpoint M of a line segment with endpoints P(x1, y1) and Q(x2, y2) is found using the equations:

Mx = (x1 + x2) / 2

My = (y1 + y2) / 2

We can rearrange these equations to solve for the missing coordinates of point Q:

x2 = 2Mx - x1

y2 = 2My - y1

Given the midpoint M(1, -2) and point P(-3, 2), we can substitute into the equations:

x2 = 2(1) - (-3) = 2 + 3 = 5

y2 = 2(-2) - 2 = -4 - 2 = -6

Therefore, the coordinates of point Q are (5, -6). The correct option is C.