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.
P(4,6) and Q(8,3)
Given C =(8,6) and A =(0,0)
The distance to C from X-axis =6 units
∴ BC =AD =6 units
The distance to C from Y -axis =8 units
∴ AB = CD =8 units
∵ B lies on X -axis and AB =8
∴ coordinate of B =(8,0)
and D lies on Y -axis and AD =6
∴ D =(0,6)
∴ B =(8,0) and D =(0,6)
Given P is mid point of CD and Q is mid point of BC.
∵ CD = 8 units ∴ CP = 4 units
and CD is parallel to X-axis , so y-coordinates of P will be equal to y-coordinate of C.
∴ y-coordinate of P = 6
x-coordinate of P = x-coordinate of C -4
= 8-4
= 4
∴ P = (4,6)
∵ BC = 6 units ∴ BQ = 3 units
and BC is parallel to Y-axis , so x-coordinates of Q will be equal to x-coordinate of B.
∴ X-coordinate of Q = 8
and y-coordinate of Q = y-coordinate of B +3
= 0+3
= 3
∴ Q = (8,3)