Question

Pleaseeeee helpppppp!!

Answer 1

Answer:  The equation of the circle as specified is (x+5)² + (y -1)² = 25

Step-by-step explanation:  Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location: A(-1,4), B(-1,1) and C(-5,1)  

subtract y-values of A & B 4-1=3 AB = 3

subtract x-values of B &C -5-(-1) =4 BC=4  3² + 4² = 9 + 16 = 25  

√25 = 5   AC = 5  That is the radiuus of the circle.    

The sides of the triangle are AB=3, BC=4, AC=5.

Use the equation for a circle:

( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

Use the coordinates of C, (-5, 1) as h and k in the equation

Substituting those values, we have (x -[-5])² + (y -[1])² = 5²

Simplify:  (x+5)² + (y -1)² = 25

A graph of the circle is attached. The radius is AC, between the center C (-5,1) and A( -1,4) on the circumference.  (Sorry, I still need to learn how to create line segments!)