Question

find the circumference of a
triangle having
vertices (2,2), (6,6)and (5,7)

Answer 1

Answer:

This us example for this question ok

Step-by-step explanation:

Step 1 :

Given coordinates A(1,3),B(5,5),C(7,5)

Finding the midpoint of AB

=(

2

5+1

,

2

3+5

)

=(3,4)

Now by finding the slope of AB=(

5−1

5−3

=

2

1

)

Now , slope of perpendicular bisector is negative reciprocal of AB that is slope of the bisector =−2.

Step 2 :

Finding the equation of AB with slope -2 and the point (3, 4) is

y−4=(−2)(x−3)

y−4=−2x+6

2x+y=4+6

2x+y=10 is equation of the bisector of AB.

Similarly, if we find the equation of bisector of AC we have

Equation of bisector of AC=>3x+y=16

Step 3 :

When we solve the given set of equations , we have

2x+y=10

3x+y=16

x=6 and y=−2

Step 4 :

Hence the coordinates of the circumcenter of the given triangle is (6,−2)

Answer :

(6,−2)