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3 years ago

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

Mathematics

1 answer:

zmey [24]3 years ago

5 0

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

<h3>The length of each side of the triangle</h3>

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

<h3>The slope of each side of the triangle</h3>

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

<h3>Classify the triangle</h3>

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

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