Question

Select all the correct answers. LMN has vertices I(-2,4) M(3,2), and N(1,-3), which describe the triangle?O rightO isoscelesO obtuse O acuteO equilateralO scalene

Answer 1

Given

The coordinates of the vertices are given

L(-2,4) M(3,2), and N(1,-3).

Step-by-step explanation

Find LM,

`\begin{gathered} LM=√((2-4)^2+(3-(-2)^2) \\ LM=√(4+25) \\ LM=√(29) \end{gathered}`

Find MN,

`\begin{gathered} MN=√((-3-2)^2+(1-3)^2) \\ MN=√(25+4) \\ MN=√(29) \end{gathered}`

FInd NL,

`\begin{gathered} NL=√((1-(-2))^2+(-3-4)^2) \\ NL=√(3^2+7^2) \\ NL=√(58) \end{gathered}`

Answer

LM=MN, two sides of the triangle are equal.

That means isosceles triangle.

And also,

`LM^2+MN^2=NL^2`

The right triangle exists , pythagoras theorem satisfies.

The answer are right trinangle, and isosceles.