Question

3. The coordinates triangle ABC arw A(1,2) B(6, 7) C(7,2)
(a) Find the equation of the perpendicular bisectors of -
i) AB
ii)BC
b) Hence find the coordinates of the point equidistant from A,B,C
​

Answer 1

Step-by-step explanation:

Given points are,

A=(−2,3),B=(2,1),C=(1,2)

To find out the circumcenter we have to solve any two bisector equations and find out the intersection points.

So, mid-point of AB = (

2

−2+2

,

2

3+1

)=(0,2)

Slope of AB is

2+2

1−3

=−

2

1

Slope of the bisector is the negative reciprocal of the given slope.

So, the slope of the perpendicular bisector =2

⇒ Equation of a line(perpendicular to AB) with slope 2 and the coordinates (0,2) is,

y−2=2x

⇒2x−y+2=0 ........ (i)

Similarly,

So, mid-point of BC = (

2

1+2

,

2

2+1

)=(3/2,3/2)

Slope of BC is

1−2

2−1

=−1

So, the slope of the perpendicular bisector =1

Equation of a line(perpendicular to BC) with slope 1 and the coordinates (3/2,3/2) is,

(y−3/2)=(x−3/2)

⇒x=y ........ (ii)

Solving Eq (i) and (ii) gives (x,y)=(−2,−2) which is the circumcentre of the given triangle