Question

The coordinates of one end of a diameter of a circle are $(5,-7)$. If the coordinates of the centre be $(7,3)$, the co ordinates of the other end of the diameter are

• A. $(6,-2)$
• B. $(9,13)$
• C. $(-2,6)$
• D. $(13,9)$

Answer 1

The correct option is B $(9,13)$

The centre of the circle lies at the mid point of the diameter.

Let the other end of the diameter be $(x,y)$.

Midpoint of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Using this formula, mid point of the diameter $=(\frac{5+x}{2},\frac{-7+y}{2})=(7,3)$

$=>\frac{5+x}{2}=7;\frac{-7+y}{2}=3$

$=>5+x=14;-7+y=6$

$=>x=9;y=13$

Hence, the other end of the diameter is $(9,13)$.