Question

(a) If two vertices of a parallelogram are
(3, 2) and ( 1, 0) and the diagonals
intersect at (2, - 5) then find the other
two vertices.​

Answer 1

Answer:

(1, - 12), (3, - 10)

Step-by-step explanation:

One of the properties of parallelogram is "The diagonals of parallelograms bisect each other".

The coordinates of midpoint are [($x_{1}$ + $x_{2}$)/2, ($y_{1}$ + $y_{2}$)/2]

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Let A (3, 2) and B (1, 0) are two vertices of a parallelogram, and O (2, -5) is the diagonals intersect.

AO = OC

$\frac{3+x}{2}$ = 2 ⇒ x = 1

$\frac{2+y}{2}$ = - 5 ⇒ y = - 12

C (1, - 12)

BO = OD

$\frac{1+x}{2}$ = 2 ⇒ x = 3

$\frac{0+y}{2}$ = - 5 ⇒ y = - 10

D (3, -10)