Question

If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is

(a) 7
(b) 5
(c) −7
(d) −8

Answer 1

The value of y for vertex S in parallelogram PQRS is found by using the properties of a parallelogram to be 5. Option B is the correct answer.

Step-by-step explanation:

To determine the value of y for vertex S in parallelogram PQRS, we can use the properties of a parallelogram, which state that opposite sides are equal in length and parallel. Since PQ is parallel to SR, and PR is parallel to QS, we need the coordinates of S to ensure the two conditions are satisfied.

Firstly, by considering the horizontal distance, since Q (0, 3) to P (2, 4) is a move of 2 units to the right, R (3, 6) to S must also be 2 units to the right, which confirms that S has an x-coordinate of 5.

Secondly, examining the vertical distance, P (2, 4) to R (3, 6) is a move of 2 units upwards. Therefore, to ensure that PQ is parallel and equal in length to SR, Q (0, 3) to S (5, y) must be a move of 2 units upwards as well, which means the y-coordinate of S must be 3 + 2, which is 5.

Therefore, the correct value of y for vertex S is (b) 5.