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).

Explanation

Find LM,

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

Find MN,

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

FInd NL,

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

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.