Mathematics, 28.07.2020 22:01 laqu33n021

Right triangle ABC is located in A(-1,-2), B(-1,1) and C(3,1) on a coordinate plane. what is the equation of a circle with radius AC? A) (x+1)2+(y+2)2=9
B) (x+1)2+(y+2)2=25
C) (x-3)2+(y-1)2= 16
D) (x-3)2+(y-1)2=25

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Answer from: hannahsparks7073

The equation of the circle is (x+1)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,-2), B(-1,1) and C(3,1) 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.

As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center. h is -1, k is -2 The radius 5, squared becomes 25.

Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .

When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.

We end up with the equation for the circle as specified:

(x+1)²+(y+1)² = 25

A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)

Right triangle ABC is located in A(-1,-2), B(-1,1) and C(3,1) on a coordinate plane. what is the equ

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Answer from: Quest

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Right triangle ABC is located in A(-1,-2), B(-1,1) and C(3,1) on a coordinate plane. what is the equ...

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