Question

D
B
с
(1,3), B(-1, 1) and C(7,-3) are the vertices of AABC. Find the
coordinates of circumcenter P and radius of circumcircle.​

Answer 1

Answer:

P(3, - 1)

Step-by-step explanation:

- The circumcenter of a triangle is the point where the three perpendicular bisectors of a triangle meet ;  

- Formula of coordinates of a midpoint of a segment with endpoints ( $x_{1}$ , $y_{1}$ ) and ( $x_{2}$ , $y_{2}$ ) is ( $\frac{x_{1} +x_{2} }{2}$ , $\frac{y_{1} +y_{2} }{2}$ ) ;

- Formula of slope m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

- The slopes of perpendicular lines are opposite reciprocals ( $m_{1}$ $m_{2}$ ) = - 1 .  

~~~~~~~~~~~~~~~~~~~

A(1, 3), B( - 1, 1), C(7, - 3)

$m_{AB}$ = $\frac{1 - 3}{-1-1}$ = 1

$m_{AC}$ = - 1

⇒ AB ⊥ AC ⇒ the circucenter P is midpoint of BC ⇒ P(3, - 1)