Question

The point (12,16) lies on the circle whose center is at the origin. What is the radius of this circle?

Answer 1

If you plot the point (12,16), you could draw a right triangle where the hypotenuse is the radius.

so 12^2+16^2 =r^2 (the hypotenuse)

144 + 256 = r^2

400 = r^2

20 = r

the equation of this circle would be x^2 + y^2 = 20^2

or x^2 + y^2 = 400

see screenshot!

Answer 2

To determine the radius of a circle with its center at the origin and a point (12, 16) lying on it, we can use the distance formula between the origin (0, 0) and the given point.

The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) is the origin (0, 0) and (x2, y2) is the given point (12, 16).

Plugging in the values, we have:

d = √((12 - 0)^2 + (16 - 0)^2)
= √(12^2 + 16^2)
= √(144 + 256)
= √400
= 20

Therefore, the radius of the circle is 20.