Question

If a(1,2) b(4,q) c(p,6) and d(3,5) are the vertices of a parallelogram abcd, find the value of pand q

Answer 1

p = 6 and q = 3

Step-by-step explanation:

Given by question,

The four vertices of a parallelogram are A(1, 2), B(4, q), C(p,6) and D(3,5).

To find, the value of pand q = ?

We know,

The diagonals of the parallelogram bisect each other.

∴ Mid point of diagonal BD = Mid Point of diagonal AC

Mid point of diagonal BD $=(\dfrac{4+3}{2},\dfrac{q+5}{2})$

$=(\dfrac{7}{2},\dfrac{q+5}{2})$

Mid Point of diagonal AC$=(\dfrac{1+p}{2},\dfrac{2+6}{2})$

$=(\dfrac{1+p}{2},\dfrac{8}{2})$

∴ $\dfrac{7}{2}=\dfrac{1+p}{2}$   and $\dfrac{q+5}{2}=\dfrac{8}{2}$

⇒  $\dfrac{7}{2}=\dfrac{1+p}{2}$

⇒ 1 + p = 7

⇒ p = 7 - 1 = 6

⇒$\dfrac{q+5}{2}=\dfrac{8}{2}$

⇒ q + 5 = 8

⇒ q  = 8 - 5 = 3

Hence, p = 6 and q = 3

Answer 2

Answer:

p=3 q=6

Step-by-step explanation: