Question

Right triangle ABC is located at A (−1, 4), 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 − 4)2 = 9
(x + 5)2 + (y − 1)2 = 25
(x + 5)2 + (y − 1)2 = 16
(x + 1)2 + (y − 4)2 = 25

Answer 1

The circle is in A, so (-1, 4) coords

(x - xo)² + (y - yo)² = r²

(x - (-1))² + (y - 4)² = r²

(x + 1)² + (y - 4)² = r²

And the radius is the length of segment AC

distance of AC is

$\sqrt{(yc-ya)^2+(xc-xa)^2}$

$\sqrt{(1-4)^2+(-5-(-1))^2}$

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

$\sqrt{9+16}$

$\sqrt{25}$

$5$

So r = 5

(x + 1)² + (y - 4)² = 5²

(x + 1)² + (y - 4)² = 25