Question

PQ is the diameter of a circle whose centre is (3,–4) & Q is (1, 4) , then the coordinates of point P will be​

Answer 1

Hellow friends

I am going to solve the question

firstly It is given that

The co ordinates of the centre is (3,-4) and Q ( 1,4)

Also given that, PQ is the diameter of the circle

Let the co ordinate of P (x, y)

According to the question

Mid point of OP = Mid point of OQ

We use the mid point formula

( X1 + X2 /2 , Y1 + Y2 /2 ) = ( X1 + X2 / 2 , Y1 + Y2 / 2 )

(3+x /2 , - 4 + y /2 ) =(3+1/2 , -4+4/2 )

(3+x/2, -4+y /2) = ( 4/2 , 0/2 )

(3+x / 2 , -4+ Y / 2 ) =(2 , 0 )

Now take LHS with LHS side

and take RHS with RHS side

2=3+x / 2 , 0=-4+y / 2

2×2 = 3+ x , 0×2 =-4 + y

4 = 3+x , 0 = -4+ y

4-3 =x , 0+4= y

1 =x or x=1 , 4 = y or y=4

Therefore , the co ordinate of p ( 1 , 4)

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