Question

use the given coordinates to compute the perimeter of the triangle. round your answer to the nearest tenth
(1 point)
the perimeter is approximately □ units.

Explanation:

Step1: Calculate the length of \( PR \)

Use the distance formula for horizontal line (\( y - \)coordinates are the same). \( PR=\vert x_{P}-x_{R}\vert=\vert1 - (-4)\vert = 5\)

Step2: Calculate the length of \( PQ \)

Use the distance formula for vertical line (\( x - \)coordinates are the same). \( PQ=\vert y_{Q}-y_{P}\vert=\vert6 - 2\vert = 4\)

Step3: Calculate the length of \( QR \)

Use the distance formula \( d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\). Here \( x_{1}=-4,y_{1}=2,x_{2}=1,y_{2}=6\).
\( QR=\sqrt{(1 - (-4))^{2}+(6 - 2)^{2}}=\sqrt{5^{2}+4^{2}}=\sqrt{25 + 16}=\sqrt{41}\approx6.4\)

Step4: Calculate the perimeter

Perimeter \(=PR + PQ+QR\). Substitute the values: \(5 + 4+6.4 = 15.4\)

Answer:

\(15.4\)