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