Prove that the following points (in each case are the vertices of a ri

1.	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» Answer: 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 42+62=52 so the distance is √52 The distance between B and C: 9⇒5=4 −8⇒−2=6 42+62=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

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»

Answer:

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 42+62=52 so the distance is √52

The distance between B and C:

9⇒5=4 −8⇒−2=6 42+62=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