Lesson Explainer: Midpoints And Perpendicular Bisectors - Nagwa

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Example 1: Finding the Midpoint of a Line Segment given the Endpoints

Given 𝐴(4,8) and 𝐵(6,6), what are the coordinates of the midpoint of 𝐴𝐵?

Answer

We recall that the midpoint 𝑀 of a line segment is the point halfway between the endpoints, which we can find by averaging the 𝑥- and 𝑦-coordinates of 𝐴 and 𝐵 respectively. Thus, we apply the formula: 𝑀(𝑥,𝑦)=𝑥+𝑥2,𝑦+𝑦2=4+62,8+62=(5,7).

Therefore, the coordinates of the midpoint of 𝐴𝐵 are (5,7).

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