The side of a square ABCD is parallel to the x-axis. Find the slopes of all its sides.

Also, find :

(i) the slope of the diagonal AC,

(ii) the slope of the diagonal BD.

Since, AB is parallel to x-axis, it's slope will be equal to the slope of x-axis.

Slope of AB = 0.

We know that,

Angle in square = 90°.

So,

AD and BC are inclined at an angle of 90° from AB so also from x-axis. (As AB || x-axis).

Slope of AD and BC = tan 90° (which is not defined).

Since, opposite sides of square are parallel.

So, CD is parallel to AB.

∴ Slope of CD = Slope of AB = 0.

(i) Diagonals of a square bisect the angle between sides.

∴ AC is inclined at an angle of 45° (anticlockwise) from AB so also from x-axis. (As AB || x-axis).

Slope of AC = tan 45° = 1.

(ii) BD is inclined at an angle of 45° (clockwise) from AB so also from x-axis. (As AB || x-axis).

Slope of BD = tan (-45°) = -1.

Hence, slope of AD and BC is not defined, slope of CD and AB = 0, slope of AC = 1 and slope of BD = -1.