Question

Triangle DEF has vertices located at D (2, 1), E (3, 5), and F (6, 2).

Answer 1

The vertices D, E and F in the triangle DEF are the coordinates of the triangle

The triangle DEF can be classified as an isosceles triangle

The length of each side of the triangle

The vertices of the triangle are given as:

D = (2, 1)

E = (3,5)

F = (6,2)

The side length of the triangle is calculated using:

L = √[(x₁ - x₂)² + (y₁ - y₂)²]

So, we have:

DE = √[(5 - 1)² + (3 - 2)²]

DE = √17

DF = √[(2 - 1)² + (6 - 2)²]

DF = √17

EF = √[(2 - 5)² + (6 - 3)²]

EF = √18

Hence, the side lengths of the triangle DEF are √17, √17 and √18

The slope of each side of the triangle

The slope of the lengths is calculated using:

m = (y₁ - y₂)/(x₁ - x₂)

So, we have:

DE = (5 - 1)/(3 - 2)

DE = 4

DF = (2 - 1)/(6 - 2)

DF = 1/4

EF = (2 - 5)/(6 - 3)

EF = -1

Hence, the slopes of the sides are 4, 1/4 and -1

Classify the triangle

In (a) and (b) above, we have sides DE and DF to be congruent and  none of the slopes are equal ot opposite reciprocals

Hence, the triangle DEF is an isosceles triangle

Read more about triangles at:

brainly.com/question/388810