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Question

The side AB 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.

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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 = negative fraction numerator 1 over denominator s l o p e space o f space A B end fraction equals fraction numerator negative 1 over denominator 0 end fraction equals n o t space d e f i n e d

As AD AB, slope of AD = negative fraction numerator 1 over denominator s l o p e space o f space A B end fraction equals fraction numerator negative 1 over denominator 0 end fraction equals n o t space d e f i n d e d

(i) The diagonal AC makes an angle of 45 with the positive direction of x axis.

s l o p e space o f space A C equals tan 45 degree equals 1

(ii) The diagonal BC makes an angle of -45 with the positive direction of x axis.

s l o p e space o f space B C equals tan open parentheses negative 45 degree close parentheses equals negative 1


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