wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the circumcentre of the triangle formed by the points (2,3), (1,-5) and (-1,4)


Open in App
Solution

Step 1. Find the equation of the perpendicular bisector of the line AB

Given three points is A(2,3), B(1,-5) and C(-1,4)

Mid point of AB,D=2+12,3-52=32,-1

Slope of AB=y2-y1x2-x1=-5-31-2=-8-1=8

Therefore, slope of the perpendicular bisector =-18

Therefore equation of the perpendicular bisector of AB with slope =-18 and passing coordinate 32,-1

y-y1=m(x-x1)⇒y+1=-18(x-32)⇒y+1=-116(2x-3)⇒16y+16=-2x+3⇒2x+16y=-13→(1)

Step 2. Find the equation of the perpendicular bisector of the line AC

Mid point of AC,E=2-12,3+42=12,72

Slope of AC=y2-y1x2-x1=4-3-1-2=-13

Therefore, slope of the perpendicular bisector =3

Therefore equation of the perpendicular bisector of the line AC with respect to slope =3 and passing through the coordinate 12,72

y-y1=m(x-x1)⇒y-72=3(x-12)⇒2y-7=3(2x-1)⇒2y-7=6x-3⇒6x-2y=-4→(2)

Step 3. Find the circumcenter

Now multiplying equation (2) with 8 and adding it with equation (1) we get

48x-16y=-32→(3)2x+16y=-13

We get x=-910

Putting the value of x in equation (1) we get y=-710

Hence, the circumcenter of triangle is -910,-710.


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equation of a Plane - Normal Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon