Question

A circle is centered at D(-1,3). The point G(-10,1) is on the circle.

Where does the point J(-3, 12) lie?

Answer 1

Answer:on the circle

Step-by-step explanation:

Answer 2

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

What is a circle?

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

$\rm (x-h)^2+(y-k)^2=r^2$

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

$\rm (x+1)^2+(y-3)^2=r^2$

Put the point on the circle equation to get the radius of the circle:

$\rm (-10+1)^2+(1-3)^2=r^2$

$\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units$

Equation of circle is:

$\rm (x+1)^2+(y-3)^2=85$

Now put the point J(-3, 12 ) in the circle equation:

$\rm (-3+1)^2+(12-3)^2=85$

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

Learn more about circle here:

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