Question

The centre of a circle is (-4, 2). If one end of the diameter of the circle is (-3, 7) then find the other end.

• A. (-4, 4)
• B. (3, 3)
• C. (-5, 3)
• D. (-5 -3)

Answer 1

The correct option is D (-5 -3)

Let the other end of the diameter B be (a, b)
We know, mid-point of a line is$=[\frac{(x_1+x_2)}{2},\frac{y_1+y_2}{2}]$

So,
$(-4,2)=[\frac{(-3+a)}{2},\frac{(7+b)}{2}]$

Now,
$\Rightarrow \frac{(-3+a)}{2}=-4$
$\Rightarrow -3+a=-8$
$\Rightarrow a=-8+3$
$\Rightarrow a=-5$

also,
$\Rightarrow \frac{(7+b)}{2}=2$
$\Rightarrow 7+b=4$
$\Rightarrow b=4–7$
$\Rightarrow b=-3$

Hence, the other end of the diameter is (-5, -3).