Midpoint Formula Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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The midpoint of segment PQPQ is M(3,−1)M(3, -1). If P=(−2,4)P = (-2, 4), find the coordinates of QQ.

Solution

  1. 1
    Use the midpoint formula in reverse. If M=(xP+xQ2,yP+yQ2)M = \left(\frac{x_P + x_Q}{2}, \frac{y_P + y_Q}{2}\right), then xQ=2⋅xM−xPx_Q = 2 \cdot x_M - x_P and yQ=2⋅yM−yPy_Q = 2 \cdot y_M - y_P.
  2. 2
    Calculate: xQ=2(3)−(−2)=6+2=8x_Q = 2(3) - (-2) = 6 + 2 = 8.
  3. 3
    yQ=2(−1)−4=−2−4=−6y_Q = 2(-1) - 4 = -2 - 4 = -6.

Answer

Q=(8,−6)Q = (8, -6)
Working the midpoint formula backwards is a common technique. Since the midpoint averages the endpoints, doubling the midpoint and subtracting the known endpoint gives the unknown endpoint.

About Midpoint Formula

A formula for finding the point exactly halfway between two points in the coordinate plane, by averaging their coordinates.

Learn more about Midpoint Formula →

More Midpoint Formula Examples

Example 1 easy

Find the midpoint of the segment joining [formula] and [formula].

Example 3 easy

Find the midpoint of the segment joining [formula] and [formula].

Example 4 easy

A circle has diameter endpoints [formula] and [formula]. Find the coordinates of the centre of the c

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