Question

The coordinates of the centre of a circle are $(-6,1.5)$. If the ends of a diameter are $(-3,y)$ and $(x,-2)$ then:

• A. $x=9,y=5$
• B. $x=5,y=-9$
• C. $x=-9,y=5$
• D. $x=-9,y=-5$

Answer 1

The correct option is C $x=-9,y=5$

The center of the circle lies at the midpoint of the diameter.

Mid-point 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 $(3,y)$ and $(x,2)$ will be,

$(-6,1.5)=(\frac{-3+x}{2},\frac{y-2}{2})$

$\Rightarrow \frac{-3+x}{2}=-6$ and $\frac{y-2}{2}=1.5$

$\Rightarrow -3+x=-12$ and $y-2=3$

$\Rightarrow x=-9$ and $y=5$