Question

Which classification describes AMNO with vertices M(2, -3), N(3, 1), and O(-3, 1)?

Answer 1

For the triangle ΔMNO, you know the coordinates of the three vertices:

M(2,-3)

N(3,1)

O(-3,1)

To be able to classify the triangle you have to calculate the length of each side. You can use the formula to determine the distance between to points to determine the side lengths:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Side MN

The coordinates of the endpoints are:

M(2,-3), N(3,1)

`\begin{gathered} d=\sqrt[]{(3-2)^2+(1-(-3))^2} \\ d=\sqrt[]{1^2+4^2} \\ d=\sqrt[]{1+16} \\ d=\sqrt[]{17} \end{gathered}`

Side NO

The coordinates of the endpoints are:

N(3,1) and O(-3,1)

`\begin{gathered} d=\sqrt[]{(3-(-3))^2+(1-1)^2} \\ d=\sqrt[]{6^2+0^2} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}`

Side OM

The coordinates of the endpoints are

M(2,-3) and O(-3,1)

`\begin{gathered} d=\sqrt[]{(2-(-3))^2+(-3-1)^2} \\ d=\sqrt[]{5^2+(-4)^2} \\ d=\sqrt[]{25+16} \\ d=\sqrt[]{41} \end{gathered}`

The side lengths of the triangle are:

MN=√17 units

NO=6 units

OM=√41 units

The sides of the triangle have different lengths, you can classify it as scalene.