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प्रश्न
Show that points A(– 4, –7), B(–1, 2), C(8, 5) and D(5, – 4) are the vertices of a parallelogram ABCD
उत्तर
We know that, slope of line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of side AB = `(2 - (-7))/(-1 - (-4))`
= `(2 + 7)/(-1 + 4)`
= `9/3`
= 3 ......(i)
Slope of side BC = `(5 - 2)/(8 - (-1))`
= `3/(8 + 1)`
= `3/9`
= `1/3` ......(ii)
Slope of side CD = `(-4 - 5)/(5 - 8)`
= `(-9)/(-3)`
= 3 .....(iii)
Slope of side AD = `(-4 - (-7))/(5 - (-4))`
= `(-4 + 7)/(5 + 4)`
=`3/9`
= `1/3` ......(iv)
∴ Slope of side AB = Slope of side CD ......[From (i) and (iii)]
∴ Side AB || side CD
∴ Slope of side BC = Slope of side AD .......[From (ii) and (iv)]
∴ Side BC || side AD
Both the pairs of opposite sides of ABCD are parallel
∴ ▢ABCD is a parallelogram.
∴ Points A(– 4, – 7), B(– 1, 2), C(8, 5) and D(5, – 4) are the vertices of a parallelogram.
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