The vertices of a parallelogram PQRS are P(a,7) Q(7,5,),R(0,4)andS(6,2). Calculate the value of a

Answer 1

To find the value of 'a', we can use the fact that opposite sides of a parallelogram are equal in length.

The distance formula between two points (x1, y1) and (x2, y2) is given by:
distance = √((x2-x1)^2 + (y2-y1)^2)

Using this formula, we can calculate the lengths of the sides of the parallelogram PQRS:

Side PQ:
Distance PQ = √((7-a)^2 + (5-7)^2)

Side RS:
Distance RS = √((6-0)^2 + (2-4)^2)

Since PQRS is a parallelogram, Side PQ is equal to Side RS. Therefore:

√((7-a)^2 + (5-7)^2) = √((6-0)^2 + (2-4)^2)

Squaring both sides, we get:

(7-a)^2 + (5-7)^2 = (6-0)^2 + (2-4)^2
(7-a)^2 + 2^2 = 6^2 + (-2)^2
(7-a)^2 + 4 = 36 + 4
(7-a)^2 = 36

Taking the square root of both sides, we get:

7-a = ±6
a = 7 - 6 or a = 7 + 6
a = 1 or a = 13

Therefore, the value of 'a' can be either 1 or 13.