Question

Show that the points (7.10), (-2, 5) and (3, - 4) are vertices of an
isosceles right triangle.​

Answer 1

HEY! YAH AAJ KE PAPER KA QUESTION HAI......

APPLY DISTANCE FORMULA

name the points as A(7,10), B (-2,5) C (3,-4)

AB =√106 , BC=√106 , AC = √212

BUT PLEASE DO CALCULATE BECAUSE..... I GUESSED..... OKAY.... HOPE YOU LIKE IT...

AT THE LAST AB = BC AND HENCE IT IS AN ISOSCELES RIGHT TRIANGLE.

Answer 2

Answer:

Hey Buddy here's ur answer

Let the given points be A(7, 10), B(-2, 5) and C(3, -4), then

AB2 = (-2 - 7)² + (5 - 10)²

⇒ AB2 = (-9)² + (-5)²

⇒ AB2 = 81 + 25 = 106

BC2 = {3 - (-2)}² + (-4 -5)²

⇒ BC2 = (3 + 2)² + (-4 - 5)²

⇒ BC2 = (5)² + (-9)²

⇒ BC2 = 25 + 81 = 106

and CA2 = (7 - 3)2 = {10 - (-4)}²

⇒ CA2 = (4)² + (10 + 4)²

=>CA2 = (4)²+ (14)2 = 16 + 196 = 212

Now,

AB2 + BC2 = 106 + 106

=> AB2 + BC2 = 212 = CA²

∴ ∠B = 90°

[By converse of Pythagoras theorem]

and AB = BC

Hence, A, B and C are the vertices of isosceles right angle triangle.