Question

The co-ordinates of one end of a diameter of a circle are $(5,-7)$. If the co-ordinates 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 $(x,y)and(5,-7)=(\frac{x+5}{2},\frac{y-7}{2})$
So,$(\frac{x+5}{2},\frac{y-7}{2})=(7,3)$
$=>x+5=7\times 2$ and $y-7=3\times 2$
$=>x=9;y=13$
Thus, the other end of the diameter is $(9,13)$.