Question

The triangle with vertices (a,b) ,(a,a) ,(b,a) is
1) equilateral
2) isosceles
3) right angled
4) right angled isosceles

Answer 1

from the qstn it is an isosceles triangle...

Answer 2

Concept

An isosceles triangle in mathematics is a triangle which have two equal sides of same length. An equilateral triangle is a triangle which have three equal sides of same length and all angles of an equilateral are equal. A right angled triangle is a triangle which have a angle of 90 degrees

Given

The triangle with vertices (a,b) ,(a,a) ,(b,a)

Find

Type of triangle

Solution

Consider a triangle PQR with vertices (a,b) ,(a,a) ,(b,a)

P = (a,b)

Q = (a,a)

R = (b,a)

PQ = [ (a-a)2 + (b-a)2 ]1/2

= (b-a)

QR = [ (b-a)2 + (a-a)2 ]1/2

= (b-a)

PR = [ (b-a)2 + (a-b)2]1/2

= [(b-a)2 + (b-a)2]1/2

= (b-a) *21/2

As PQ=QR which states that the triangle is an isosceles triangle.

#SPJ2