Question

The endpoints of a

Answer 1

Answer:

2nd option

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the centre is at the midpoint of the endpoints of the diameter.

The coordinates of the centre is the average of the coordinates of the endpoints.

centre = ( $\frac{-4+2}{2}$, $\frac{7-1}{2}$ ) = ($\frac{-2}{2}$ , $\frac{6}{2}$ ) = (- 1, 3 )

the radius is the distance from the centre to either of the endpoints

using the distance formula to calculate r

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2$

with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )

r = $\sqrt{(2-(-1))^2+(-1-3)^2}$

  = $\sqrt{(2+1)^2+(-4)^2}$

  = $\sqrt{3^2+16}$

  = $\sqrt{9+16}$

  = $\sqrt{25}$

   = 5

then equation of circle is

(x - (- 1) )² + (y - 3)² = 5² , that is

(x + 1)² + (y - 3)² = 25