Question

Prove that the points A (-3,0) , B(1,-3) , C(4,1) are the vertices of an isosceles triangle​

Answer 1

Step-by-step explanation:

Vertices of the triangle are A(−3,0), B(1,−3), C(4,1).

Distance between two points =

( x 2 −x 1 ) 2 +(y 2 −y1) 2

AB= (1+3) 2 +(−3−0) 2 =5

BC= (4−1) 2+(1+3)2 =5

AC= (4+3) 2+(1−0) 2 =5

AB=BC

Therefore, ΔABC is an isosceles triangle.

(AB) 2 +(BC) =5

2+52=50 and (AC) 2=(5 2 ) 2=50

∴(AB)

2 +(BC) 2 =(AC) 2

So, the triangle satisfies the Pythagoras theorem and hence it is a right angled triangle.