Question

Give three points
A(3,2) , B(1,4), C(10,4) and fourth point D(x,y).
Such that these four points from a parallelogram​

Answer 1

Answer:

Given

Co-ordinates of the parallegram

A(3,2) , B(1,4), C(10,4)

To find

The fourth coordinate D(x,y)

Topic -

Coordinate geometry

Solution

➣The Diagonals of the parallegram bisect each other.

➥diagonal of Parallegram ABCD - AB and CD

➥midpoint of AB = midpoint CD

According to midpoint theorem

$\bigg(\dfrac{x_1+x_2}{2}\bigg), \bigg( \dfrac{y_1+y_2}{2}\bigg)$

Finding midpoint of AC

$⟹ \bigg( \dfrac{3+1}{2}\bigg), \bigg( \dfrac{2+0}{2}\bigg)$

Midpoint of AC = 2, 1

Finding midpoint of BD

$\bigg( \dfrac{1+x}{2}\bigg), \bigg( \dfrac{4+y}{2}\bigg)$

Midpoint of BD = 1+x/2 , 4+y/2

♦ Now equate the mid-points of AC and BD

$⟹\bigg( \dfrac{1+x}{2}\bigg)= 2$

$⟹1+x = 4 \\\\ ⟹\bold\red{{x= 3}}$

So the value of x is 3

$⟹\bigg(\dfrac{4+y}{2}\bigg)= 1$

$⟹4+y =2 \\ \\ ⟹ \bold \pink{y = -2 .}$

So the value of y is -2

✏️Coordinate of D is (3,-2)

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