Question

IF TWO ADJACENT VERTICES OF A PARALLELOGRAM ARE (3,2) AND(-1,0) AND DIAGONALS INTERSECT AT (2,-5) THEN FIND THE COORDINATES OF THE OTHER TWO VERTICES

Answer 1

because the diagonal of a parallelogram intersect each other then,by the midpoint formula you can find the third and fourth vertices of a parallelogram,

Answer 2

Answer:

Coordinates of other two vertices are C(1,-12) and D(5,-10)

Step-by-step explanation:

Given the two adjacent vertices of parallelogram  A(3,2) and B(-1,0) and diagonals intersect at (2,-5) then we have to find the coordinates of other two vertices.

Let C(e,f) and D(g,h) are the other two adjacent vertices of parallelogram.

As the diagonals of parallelogram bisect each other.

Therefore, point (2,-5) is the mid point of AC and BD

$\text{The mid point of line-segment joining the points (a,b) and (c,d) is }$

$(\frac{a+c}{2},\frac{b+d}{2})$

Mid point of AC and BD given i.e

$(\frac{3+e}{2},\frac{2+f}{2})=(2,-5)=(\frac{-1+g}{2},\frac{0+h}{2})$

⇒ 3+e=4 ⇒ e=1

2+f=-10 ⇒ f=-12

-1+g=4 ⇒ g=5

0+h=-10 ⇒ h=-10

Hence, coordinates of other two vertices are C(1,-12) and D(5,-10)