Question

The side AB of a square ABCD is parallel to the x-axis. Find the slopes of all its sides. Also, find: 

1. the slope of the diagonal AC.
2. the slope of the diagonal BD.

Answer 1

We know that the slope of any line parallel to x-axis is 0.

Therefore, slope of AB = 0

As CD || BC, slope of CD = Slope of AB = 0

As BC ⊥ AB, slope of BC = `-1/"slope of AB"` = `(-1)/0` = not defined

As AD ⊥ AB, slope of AD = `-1/"slope of AB"` = `(-1)/0` = not defined

i. The diagonal AC makes an angle of 45° with the positive direction of x-axis. 

∴ Slope of AC = tan 45° = 1

ii. The diagonal BD makes an angle of – 45° with the positive direction of x-axis.

∴ Slope of BD = tan (– 45°) = −1