Question

Prove that the points (1,5).(-7, 9) and (-10, -17) are the vertices of a
right angled triangle​

Answer 1

It is proved, the points "(1,5).(-7, 9) and (-10, -17)" are the vertices of a

right angled triangle​.

Step-by-step explanation:

Let  A(1, 5), B( - 7, 9)and C( - 10,- 17) are the vertices of a triangle right angled triangle.

$AB^{2}$ = $(-7 - 1)^{2}$ + $( 9 - 5)^{2}$

= $(- 8)^{2}$ + $4^{2}$ = 64 + 16 = 80

$BC^{2}$ = $(- 10 + 7)^{2}$ + $( - 17  - 9)^{2}$

= $(- 3)^{2}$ + $( - 26)^{2}$

=  9 + 676 = 685

$CA^{2}$ = $(- 10 - 1)^{2}$ + $( - 17 - 5)^{2}$

= $(- 11)^{2}$ + $( - 22)^{2}$

= 121 + 484 = 605

∴ $AB^{2}$ + $CA^{2}$ = 80 + 605 = 685 = $BC^{2}$ ,

it is proved, the points (1,5).(-7, 9) and (-10, -17) are the vertices of a

right angled triangle​.