Question

The triangle DEF has vertices D(-1,3)
E(7,1) and F(4,6). Classify the triangle as:
a) isosceles or scalene
b) right angled or not

Answer 1

An isosceles triangle has at least two equal sides.
To check this, we find the difference between the end-points of each of the sides, and from that, we calculate the length using Pythagoras Theorem.
D-E (-1,3)-(7,1)=(-1-7,3-1)=(-8,2)
L=√(8²+2*sup2;)=√68
E-F (7,1)-(4,6)=(7-4,1-6)=(3,-5)
L=√(3²+(-5)²)=√34
F-D (4,6)-(-1,3)=(4-(-1),6-3)=(5,3)
L=√(5²+3²)=√34

Since mEF=mFD, we conclude that the triangle DEF is isosceles.

Since mEF²+mFD²=mDE², we conclude that ∠EFD is a right angle, thus the triangle is a right-triangle.

Answer 2

L=√(8²+2²)=√68