1.

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

Answer»

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)



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