Coordinate Representation Math Example 3

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Example 3

easy
Find the midpoint of the segment joining P(−4,6)P(-4, 6) and Q(8,−2)Q(8, -2).

Solution

  1. 1
    Step 1: Midpoint formula: M=(x1+x22,y1+y22)M = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right).
  2. 2
    Step 2: M=(−4+82,6+(−2)2)=(2,2)M = \left(\dfrac{-4+8}{2}, \dfrac{6+(-2)}{2}\right) = \left(2, 2\right).

Answer

Midpoint M=(2,2)M = (2, 2).
The midpoint averages the xx- and yy-coordinates separately. It represents the point exactly halfway along the segment, which can be verified by checking that the distance from each endpoint to MM is equal.

About Coordinate Representation

Describing geometric objects precisely using ordered pairs (x,y)(x, y) or triples (x,y,z)(x, y, z) in a coordinate system.

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