Question

Prove by section formula that
the points (10,-6) (2,-6) (-4,-2)
and (4,-2) taken in the order, are vertices of a parallelogram
​

Answer 1

$\huge\rm\underline\purple{Answer:-}$

.

If a point P(x,y)

divides a line joining points (x1,y1) and (x2,y2) in the ratio a:b

then(x,y)=(ax2+bx1a+b,ay2+by1a+b)

If P is the mid point then a=b=1

⇒(x,y)=(x2+x11+1,y2+y11+1)

=(x1+x22,y1+y22)

Now co−ordinates of parallelogram's vertices are given as:

A(10,−6), B(2,−6), C(−4,−2), D(4,−2)

As diagonals of parallelogram bisect each other.

⇒Mid point of AC=Mid point of BD

Now, Mid point of AC=(10−42)

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