The side AB of a square ABCD is parallel to the x−axis. Find the slopes of all its sides.
Also find:
i) The slope of diagonal AC
ii) The slope of diagonal BD
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Solution
Finding the slope of all sides of squareWe know that, the slope of any line parallel to x−axis is 0. ∴Slope ofAB=0
As, CD∥AB, ⇒Slope ofCD=Slope ofAB=0
Now, BC⊥AB (Adjacent sides of square)
We know that,
if two lines are perpendicular then product of their slope is −1.
⇒Slope ofBC=−1slope ofAB
=−10=not defined.
Similarly, AD⊥AB (Adjacent sides of square)
We know that, if two lines are perpendicular then product of their slope is −1
⇒Slope ofAD=−1slope ofAB
=−10=not defined.
Finding the slope of the diagonals of a square (i) Slope of diagonal AC
The diagonal AC makes an angle of 45∘ with the positive direction of x−axis,
⇒Slope ofAC=tan45∘=1
(ii) Slope of diagonal BD
The diagonal BD makes an angle of −45∘ with the positive direction of x−axis,
⇒Slope ofBD=tan45∘=1
Hence, slope of side ABandCD is 0,
slope of side BCandAD is not defined.
Slope of diagonals ACandBD is 1 and −1 respectively.