Find the perimeter of a triangle with points A(1,2), B(1,8), and C(5,5) on a Cartesian coordinate plane.

the distance from 1,2 to 1,8 is simply 6 units, we can read that off the grid. Now let's see what the other distances are, and add them all up to get the perimeter.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AC=\sqrt{(5-1)^2+(5-2)^2}\implies AC=\sqrt{4^2+3^2} \\\\\\ AC=\sqrt{25}\implies AC=5 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf B(\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) \\\\\\ BC=\sqrt{(5-1)^2+(5-8)^2}\implies BC=\sqrt{4^2+3^2} \\\\\\ BC=\sqrt{25}\implies BC=5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{perimeter}{6+5+5\implies 16}~\hfill[/tex]

Ajithmohan Ajithmohan · Answer 2 · 2022-06-21T18:39:36+02:00

The perimeter of a triangle with points A(1,2), B(1,8), and C(5,5) on a Cartesian coordinate plane is 16 units.

How to calculate the perimeter of the triangle with the points mentioned in the question ?

The points mentioned are A(1,2), B(1,8), and C(5,5) .

The perimeter of rectangle is calculated by adding the length of the three sides.

We have to calculate the length of the three sides by the Distance formula.

According to Distance formula, the distance between two points (x1,y1) and (x2,y2) is =

Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex] units.

Length of AB = [tex]\sqrt{(1 - 1)^{2} + (2 - 8)^{2} }[/tex] = [tex]\sqrt{6^{2} }[/tex] = [tex]6[/tex] units

Length of BC = [tex]\sqrt{(1 - 5)^{2} + (8 - 5)^{2} }[/tex] = [tex]\sqrt{16 + 9}[/tex] = [tex]5[/tex] units

Length of AC = [tex]\sqrt{(1 - 5)^{2} + (2 - 5)^{2} }[/tex] = [tex]\sqrt{16 + 9}[/tex] = [tex]5[/tex] units

Therefore the perimeter of the triangle ΔABC is = Length of sides (AB + BC + AC) = (6 + 5 + 5) units = 16 units.

The perimeter of a triangle with points A(1,2), B(1,8), and C(5,5) on a Cartesian coordinate plane is 16 units.

To learn more about perimeter of a triangle, refer -

https://brainly.com/question/2246082

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