Question

(c) The ends of diameter AB of circle are A (-2,- 7) and
B (1, -11). Find its radius and co-ordinates of centre.
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Answer 1

Answer:

Hey there.

Given that the ends of the coordinates of the ends of the diameter are

A (-2, -7) and B (1, -11)

Radius is half of the diameter.

So, first the length of the diameter must be found.

For this, we can find the distance between the coordinates A and B.

Distance formula should be applied:-

$\sqrt{x2-x1^{2}) + (y2-y1)^{2}$

$\sqrt{(1--2^{2}) + (-11--7)^{2}$

$\sqrt{(1+2^{2}) + (-11+7)^{2}$

$\sqrt{(3^{2}) + (-4)^{2}$

$\sqrt{9+16}$

$\sqrt{25}$

=5cm.

So, the diameter is 5cm.

The radius will be half of the diameter.

So, radius = $\frac{5}{2}$

radius = 2.5cm

The coordinates of center can be found by finding the midpoint of the line AB.

A (-2, -7) and B (1, -11)

Midpoint formula is $\frac{x1+x2}{2}$, $\frac{y1+y2}{2}$

$\frac{1+(-2)}{2}$, $\frac{-11+ (-7)}{2}$

= $\frac{-1}{2}$, $\frac{-18}{2}$

Coordinates of centre will be:- $\frac{-1}{2}$, 9

Hope it helps!

Stay safe and keep learning Math!