Question

Lana draws ALMN on the coordinate plane. What is the perimeter of ALMN? Round to the nearest unit

Answer 1

We are asked to determine the perimeter of triangle LMN. To do that we will use the fact that the perimeter is the sum of the length of the sides of the triangle. Therefore, we have:

`P=LM+MN+LN`

To determine the value of the length of "LM" we will use the formula for the euclidian distance:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Where:

`\begin{gathered} (x_1,y_1)_;\left(x_2,y_2\right) \\ \end{gathered}`

Are the endpoints of the segment. For LM we have that the coordinates of the endpoints are:

`L=\lparen-3,2)`
`M=(3,5)`

Substituting we get:

`d_(LM)=√((3-(-3))^2+(5-2)^2)`

Solving the operations:

`d_(LM)=√(6^2+3^2)`

Solving the operations:

`d_(LM)=√(45)`

Now, we use the endpoints of MN:

`M=(3,5)`
`N=(9,2)`

Substituting we get:

`d_(MN)=√((9-3)^2+(2-5)^2)`

Solving the operations we get:

`\begin{gathered} d_(MN)=√(6^2+\left(-3\right)^2) \\ \\ d_(MN)=√(45) \end{gathered}`

Now, we apply the equation for segment LN:

`d_(LN)=\sqrt{}(9-(-3))^2+(2-2)^2`

Solving the operations:

`d_(LN)=12`

Now, we substitute in the formula for the perimeter:

`P=√(45)+√(45)+12`

Adding like terms:

`P=2√(45)+12`

In decimal form rounded to the nearest unit this is:

`P=25`

Therefore, the perimeter of the figure is 25.