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Question

The side AB of a square ABCD is parallel to the xaxis. 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 xaxis is 0.
Slope of AB=0
As, CDAB,
Slope of CD=Slope of AB=0

Now,
BCAB (Adjacent sides of square)
We know that,
if two lines are perpendicular then product of their slope is 1.

Slope of BC=1slope of AB

=10=not defined.

Similarly,
ADAB (Adjacent sides of square)

We know that, if two lines are perpendicular then product of their slope is 1

Slope of AD=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 xaxis,

Slope of AC=tan45=1

(ii) Slope of diagonal BD

The diagonal BD makes an angle of 45 with the positive direction of xaxis,

Slope of BD=tan45=1

Hence, slope of side AB and CD is 0,
slope of side BC and AD is not defined.
Slope of diagonals AC and BD is 1 and 1 respectively.

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