Straight lines

By using the concept of slope, prove that the diagonals of a rhombus are at right angles.

2 Answers

see one very good way will be to assume that the two vertices are (0,0) and (a,0)

then the third side is parallel to the x asxis (k, c) and (k+a,c)

so we have a parallelogram

now equate the length of the third side as a

so we have

k²+c²=a²

now the slope of the diagonals have a product of

\frac{c-0}{k-a}\times\frac{c-0}{k+a-0}=\frac{c^2}{k^2-a^2}=-1

Hence proved...

yo! :D

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