Question

Prove that the following points (in each case are the vertices of a right angled isosceles triangle.
(1) (3,0), (6,4) and (-1, 3)
(2) (1, 7) (4, 2) and (-1 -1)
(3) (5,6), (1,5) and (2,1)
(4) (2,3) (- 2, 2) and (-1, -2)
(5) A(3, - 1), B(5, - 1) and C(3, - 3)

Answer 1

Answer:

1. Let A(3,0),B(6,4),C(−1,3)

AB=(x22−x21)+(y22−y11)−−−−−−−−−−−−−−−−−−√

AC=(−4)2+(3)2−−−−−−−−−−−√=25−−√=5

AB=(32)+(42)−−−−−−−−−√=25−−√=5

BC=(−7)2+(−1)2−−−−−−−−−−−−−√=52–√

Now as BC2=AC2+AB2

We can say that the given points are of a right angled isosceles triangle.

2.no

3.If we label them A(13,-2) B(9-8) and C(5-2)

The distance between A and B:

13 ⇒ 9 = 4  − 2 ⇒ − 8 = 6  4 2+ 6 2 = 52  so the distance is  √ 52

The distance between B and C:

9 ⇒ 5 = 4  − 8 ⇒ − 2 = 6  4 2 + 6 2 = 52

the distance is  √ 52  

The distance between A and C is 8 as they are both on -2 for  y

The distances AB and BC are  √ 52

and therefore isosceles.

4.No

5.yes it is an isocelus triangle