Question

What is the perimeterABC is shown on the grid.9 +27 unitsB11490 9+27 units9+ I units9+VT units

Answer 1

We have three points that represent the vertices of the triangle

- A( -1, 5 )

- B( 4, 5 )

- C( -1, 1 )

We need to calculate the distances between the points to calculate the perimeter

To calculate the distances we must use the next equation

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

Distance for AB:

`\begin{gathered} d_1=\sqrt[]{(4-(-1))^2+(5-5)^2} \\ d_1=\sqrt[]{5^2+0^2}=\sqrt[]{5^2}=5 \end{gathered}`

Distance for BC:

`\begin{gathered} d_2=\sqrt[]{(-1-4)^2+(1-5)^2} \\ d_2=\sqrt[]{(-5)^2+(-4)^2}=\sqrt[]{41} \end{gathered}`

Distance for AC:

`\begin{gathered} d_3=\sqrt[]{(-1-(-1))^2+(1-5)^2} \\ d_3=\sqrt[]{0^2+(-4)^2}=\sqrt[]{16}=4 \end{gathered}`

Finally, the perimeter is

`\begin{gathered} S=d_1+d_2+d_3 \\ S=5+\sqrt[]{41}+4 \\ S=9+\sqrt[]{41} \end{gathered}`

So, the answer is

`9+\sqrt[]{41}\text{ units}`