Math, asked by viveksingh65, 5 months ago

find the circumtance of a triangle ABC with virtices A(5,1) , B(-3,-7) and C(7,-11)​

Answers

Answered by apekshanarke29
0

Answer:

Here is ur answer

Step-by-step explanation:

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})=(

2

5−3

,

2

1−7

)

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

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

−3−5

−7−1

=1

Equation of perpendicular line bisector of AB passing through point P

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

1

−1

(x−1)

y=-x-2y=−x−2 ---------- (1)

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

2

7−3

,

2

−1−7

)

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

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

7+3

−7+1

=−

5

3

Equation of perpendicular line bisector of BC passing through point Q

y+4=-\dfrac{5}{3}(x-2)y+4=−

3

5

(x−2)

y=-\dfrac{5}{3}x-\dfrac{2}{3}y=−

3

5

x−

3

2

------------(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−

3

5

x−

3

2

=−x−2

x=2x=2

Put x=2 into y=-x-2

y=-4

Cirncumcentre: (2,-4)

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