Question

ABCD is a rectangle with vertex A(0,0) as shown in below figure where P and Q are midpoints of sides CD and BC respectively. If C =(8,6) then find the coordinates of P and Q.

• A. P(4,6) and Q(8,3)
• B. P(6,4) and Q(3,8)
• C. P(8,3) and Q(4,6)
• D. P(3,8) and Q(6,4)

Answer 1

The correct option is A

P(4,6) and Q(8,3)

Given C =(8,6) and A =(0,0)

The distance to C from X-axis =6 units

$\therefore$ BC =AD =6 units

The distance to C from Y -axis =8 units

$\therefore$ AB = CD =8 units

$\because$ B lies on X -axis and AB =8

$\therefore$ coordinate of B =(8,0)

and D lies on Y -axis and AD =6

$\therefore$ D =(0,6)

$\therefore$ B =(8,0) and D =(0,6)

Given P is mid point of CD and Q is mid point of BC.

$\because$ CD = 8 units $\therefore$ CP = 4 units

and CD is parallel to X-axis , so y-coordinates of P will be equal to y-coordinate of C.

$\therefore$ y-coordinate of P = 6

x-coordinate of P = x-coordinate of C -4

= 8-4

= 4

$\therefore$ P = (4,6)

$\because$ BC = 6 units $\therefore$ BQ = 3 units

and BC is parallel to Y-axis , so x-coordinates of Q will be equal to x-coordinate of B.

$\therefore$ X-coordinate of Q = 8

and y-coordinate of Q = y-coordinate of B +3

= 0+3

= 3

$\therefore$ Q = (8,3)