Question

find the circumcentre of∆ABC with vertices A(5,1) B(-3,-7) and C(7,-1)​

Answer 1

Step-by-step explanation:

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Answer 2

The circumcentre of∆ABC is (2,-4)

Step-by-step explanation:

The vertices of ∆ABC are A(5,1) B(-3,-7) and C(7,-1)​

Circumcentre: It is point of intersection of perpendicular bisector of each sides of triangle.

# Midpoint of side AB at P, $=(\frac{5-3}{2},\frac{1-7}{2})$

Midpoint of side AB at P, $=(1,-3)$

Slope of line AB, m $=\dfrac{-7-1}{-3-5}=1$

• Equation of perpendicular line bisector of AB passing through point P

$y+3=\dfrac{-1}{1}(x-1)$

$y=-x-2$  ---------- (1)

# Midpoint of side BC at Q, $=(\frac{7-3}{2},\frac{-1-7}{2})$

Midpoint of side BC at Q, $=(2,-4)$

Slope of line BC, m $=\dfrac{-7+1}{7+3}=-\dfrac{3}{5}$

• Equation of perpendicular line bisector of BC passing through point Q

$y+4=-\dfrac{5}{3}(x-2)$

$y=-\dfrac{5}{3}x-\dfrac{2}{3}$  ------------(2)

Point of intersection of equation (1) and equation (2) is circumcentre of triangle.

Using substitution method:-

$-\dfrac{5}{3}x-\dfrac{2}{3}=-x-2$

$x=2$

Put x=2 into y=-x-2

y=-4

Cirncumcentre: (2,-4)

#Learn more:

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