Question

Right triangle ABC is located at A (−1, −2), B (−1, 1), and C (−5, 1) on a coordinate plane. What is the equation of a circle A with radius segment AC?
(x + 1)2 + (y + 2)2 = 9
(x + 5)2 + (y − 1)2 = 16
(x + 1)2 + (y + 2)2 = 25
(x + 5)2 + (y − 1)2 = 25

Answer 1

Find the length of the line from A to C, which would be the radius using the distance formula:

Distance = √(-5 +1)^2 + 1+2)^2)

Distance = √(4^2 + 3^2)

Distance = √25

Distance = 5

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2, where h and k is the center point X and y values and r is the radius.

The center of the circle is located at A ( -1,-2) and the radius is 5.

Replace h, k and r with those values:

(x - (-1))^2 + (y- (-2))^2 = 5^2

Simplify to get:

(x+1)^2 + (y+2)^2 = 25