Question

what type of triangle formed by the points a(-5 6) b(-4 -2) and c(7 5)​

Answer 1

Answer :-

Scalene triangle

Given :-

Vertices of triangle are

• A=( -5, 6)
• B = (-4 , -2)
• C = (7, 5)

SOLUTION :-

First we find the distances between the sides of a triangle i.e AB,BC,AC

• AB = Distance between A and B
• BC = Distance between B and C
• AC = Distance between A and C

$Distance \: Formula = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$AB = \sqrt{[-5-(-4)]^2+ [6 -(-2)]^2}$

$AB =\sqrt{(-5+4)^2+(6+2)^2}$

$AB =\sqrt{(-1)^2+(8)^2}$

$AB =\sqrt{1+64}$

$AB =\sqrt{65}$

$BC = \sqrt{(-4-7)^2+(-2-5)^2}$

$BC=\sqrt{(-11)^2+(-7)^2}$

$BC =\sqrt{121+49}$

$BC =\sqrt{170}$

$AC = \sqrt{(-5-7)^2+(6-5)^2}$

$AC =\sqrt{(-12)^2+(1)^2}$

$AC =\sqrt{144+1}$

$AC =\sqrt{145}$

We shall verify the Pythagoras theorem also to verify the sides are right angle triangle .

Sum of squares of any two sides equals to square of third side.

AB² + AC² = BC²

(√65)² +(√145)² = (√170)²

65 + 145 = 170

210 ≠ 170

Hence it is not a right angle triangle.

☆As all sides are different i.e not a Equilateral triangle, Isoceles triangle, Right angle triangle , Right angle isoceles triangle.

☆So, the distance between these points are different So, the given vertices are of vertices of a scalene triangle .

Know more :-

Where three points are given and it is required to be :-

☆ Isoceles triangle - Two sides or two angles equal .

☆ Equilateral triangle - All three sides or three angles equal .

☆ Isoceles right angle triangle- Sum of squares equal to third side and two sides are equal.