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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)

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B

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

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C

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

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D

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

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Solution

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

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)


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