Question

in a city,a circular park is situated with centre O(3,3).there are two exit gates p and q which are opposite to each. the location of exit gate 'p' is (5,3)
the location of exit gate q will be

Answer 1

Answer: q=(1,3)

Step-by-step explanation:

• Given,p and q lie opposite to each other.
• So, if we join them, we find that it is the diameter.
• Coordinates of O = 3,3 (given)
• Coordinates of p = 5,3 (given)

• Let,the co-ordinates of q be (x,y)

• Now, $(\frac{x+5}{2},\frac{y+3}{2} )=(3,3)$

             ⇒ $\frac{x+5}{2}=3 \ and \ \frac{y+3}{2} =3$

            ⇒ x=6-5  and y=6-3

            ∴ x=1 and y=3.

• Hence,the co-ordinates of q is (1,3).