Math CentralQuandaries & Queries


Question from Nasreen, a student:

A(7,2) and C(1,4) are two vertices of a square ABCD
find in the form ax+by=c the equation of the diagonal BD


  1. The diagonal BD is perpendicular to AC and bisects AC. So the midpoint of AC is also a point on the equation of line BD. Find the midpoint of AC.

  2. The diagonal BD is perpendicular to AC, so its slope is the negative reciprocal of the line containing AC. Find the slope of AC and take the negative reciprocal to know the slope of BD.

  3. Now that you have the slope of BD and a point on BD (the midpoint of AC), you can use the point-slope form to create the equation for the line containing BD.

Stephen La Rocque.

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