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

The correct option for the equation of a circle A with radius segment AC is (x + 1)² + (y + 2)² = 25

The reason for the above selection is given as follows:

The given vertices of the triangle ΔABC, are:

A(-1, -2), B(-1, 1), and C(-5, 1)

The required parameter:

The equation of a circle with center at A and radius of segment AC

Method:

The length of segment AC which is the radius of the circle is found and

with the coordinates of point A and the calculated length of the radius, the

values are plugged into the general equation of a circle to arrive at the

correct answer option

The length of segment AC = √((-5 - (-1))² + (1 - (-2))²) = 5

∴ The length of segment AC = 5 = The length of the radius of circle A, r

r = 5

The general equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle = Point A(-1, -2)

∴ h = -1, and k = -2

Plugging in the values of r, h, and k, in the equation of a circle gives;

(x - h)² + (y - k)² = r² where, h = -1, k = -2, and r = 5 gives;

(x - (-1))² + (y - (-2))² = 5²

We get;

(x + 1)² + (y + 2)² = 5² = 25

Therefore, the correct option is (x + 1)² + (y + 2)² = 25

Learn more about the equation of a circle here:

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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

answer: i literally just answered this question but they want me to do it again

step-by-step explanation: