How do you find the perimeter if it's a triangle in a coordinate plane X(0,2), Y(4,-1), Z(-2,-1)?

Question

Mason Adams · Accepted Answer

#color(indigo)("Perimeter of the triangle XYZ " = 14.61 " sq units"# #"Distance between two points, knowing their coordinates "# #d = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)# #X (0,2), Y (4,-1), Z(-2,-1)# #bar (XY) = z = sqrt((4-0)^2 + (-1-2)^2) = 5# #bar(YZ) = x = sqrt((-2-4)^2 + (-1+1)^2 = 6# #bar(XZ) = y = sqrt((-2-0)^2 + (-1-2)^2) = 3.61# #color(indigo)("Perimeter of the triangle XYZ " = z + x + y = 5 + 6 + 3.61 = 14.61 " sq units"#

Claire Akin · Answer

undefined To find the perimeter of the triangle given its vertices in the coordinate plane, you can use the distance formula to calculate the lengths of each side and then sum them up.

The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Using this formula, you can find the lengths of the sides XY, YZ, and XZ, and then sum them to get the perimeter of the triangle.

$$ \text{Distance XY} = \sqrt{(4 - 0)^2 + (-1 - 2)^2} $$

$$ \text{Distance YZ} = \sqrt{(-2 - 4)^2 + (-1 - (-1))^2} $$

$$ \text{Distance XZ} = \sqrt{(-2 - 0)^2 + (-1 - 2)^2} $$

Then, add these distances together to find the perimeter of the triangle.

$$ \text{Perimeter} = \text{Distance XY} + \text{Distance YZ} + \text{Distance XZ} $$

Calculating each distance and summing them up will give you the perimeter of the triangle.