Question

A(-1,1),B(5,3) are opposite vertices of a square in the XY-plane. Find the equation of the other diagonal f the square

Answer 1

Step-by-step explanation:

As shown in the attached figure below, A(-1, 1) and B(5, 3) are opposite vertices of the square ACBD. AB and CD are the two diagonals of the square intersecting at the point O.

We are to find the equation of diagonal CD.

We know that the diagonals of a square bisect each other perpendicularly.

So, AB is perpendicular to CD and O is the midpoint of both AB and CD.

The co-ordinates of point O are given by

And, the slope of the diagonal AB is given by

We know that the product of the slopes of two perpendicular lines is -1.

So, the slope of diagonal CD (m') is calculated as follows :

Therefore, the equation of diagonal CD with slope m' and passing through the point O(2, 2) is given by

Thus, the required equation of the other diagonal is