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Question
Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7). Show that ABCD is a trapezium.
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Solution
Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7) are the vertices of a quadrilateral.
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(-4 + 4)/(9 - 3) = 0/6`= 0
Slope of BC = `(-7 + 4)/(5 -9)= (-3)/(-4) = 3/4`
Slope of CD = `(-7 + 7)/(7 - 5) = 0/2` = 0
Slope of AD = `(-7 + 4)/(7 - 3) = (-3)/4 = - 3/4`
The slope of AB and CD are equal.
∴ AB is parallel to CD. Similarly, the slope of AD and BC are not equal.
∴ AD and BC are not parallel.
∴ The Quadrilateral ABCD is a trapezium.
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