Question

Prove that the points (4, 5) (7, 6) (4, 3) (1, 2) are the vertices of a parallelogram.

Answer 1

Answer:

ABCD is a Parallelogram

Step-by-step explanation:

parallel lines have same slopes

let A(4,5) B(7,6) C(4,3) and D(1,2)

Slope of AB = 6-5 / 7-4 = 1/3

Slope of CD = 3-2 / 4-1 = 1/3

therefore,  AB||CD

Slope of AD = 5-2 / 4-1 = 3/3 = 1

Slope of BC = 6-3/7-4 = 3/3 = 1

therefore, AD||BC

Opposite sides are parallel to each other.

Hence, ABCD is a parallelogram.