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?
A. (x - 1)^2 + (y - 4)^2 = 25
B. (x + 5)^2 + (y + 1)^2 = 16
C. (x + 1)^2 + (y + 4)^2 = 25

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sqdancefan sqdancefan · Answer 1 · 2023-05-22T02:50:44+02:00

Answer:

A. (x - 1)^2 + (y - 4)^2 = 25

Step-by-step explanation:

Given points A(1, 4) and C(5, 1), you want the equation of circle A with radius AC.

The equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

Circle A has its center at point A, so the equation is ...

(X -1)² +(y -4)² = r²

We don't need to know the value of r² to choose the correct answer:

(x -1)² +(y -4)² = 25

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Additional comment

The difference C -A is (5 -1, 1 -4) = (4, -3). This means the square of the radius is r² = 4² +(-3)² = 25, matching the equation we chose.

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