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 =(5,6) then find the coordinates of P and Q.

Answer 1

Given C =(5,6) 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 =5 units

$\therefore$ AB = CD =5 units

$\because$ B lies on X -axis and AB =5

$\therefore$ coordinate of B =(5,0)

and D lies on Y -axis and AD =6

$\therefore$ D =(0,6)

$\therefore$ B =(5,0) and D =(0,6)

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

$\because$ CD = 5 units $\therefore$ CP = 2.5 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 -2.5

= 5-2.5

= 2.5

$\therefore$ P = (2.5,6)

$\because$ 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 = 5

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

= 0+3

= 3

$\therefore$ Q = (5,3)