ABCD is a square where $\mathrm{B}(1,3), \mathrm{D}(3,2)$ are the end points of the diagonal BD . Find: the equation of the diagonal AC
Explanation
Since ABCD is a square, the diagonals AC and BD are perpendicular bisectors of each other. The midpoint of the diagonal BD is ((1+3)/2, (3+2)/2) = (2, 2.5). The slope of the diagonal BD is (2-3)/(3-1) = -1/2. The slope of the diagonal AC is the negative reciprocal of the slope of the diagonal BD, which is 2. The equation of the diagonal AC is y - 2.5 = 2(x - 2), which simplifies to y = -x + 4.
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