Mathematics
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.
Straight Line Eq
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Answer
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.
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