Answer:
14.47 . . . units
Step-by-step explanation:
Given the vertices of triangle XYZ are (-1, 3), (3, 0) and (-1, -2), you want the perimeter rounded to hundredths.
Perimeter
The perimeter of a polygon is the sum of the lengths of the sides. When the points defining a side are on a vertical line, as with segment XZ, the length is the difference of y-coordinates.
When the points are not on a horizontal or vertical line, the distance between them can be found using the distance formula.
Distance formula
The distance between (x1, y1) and (x2, y2) is given by the formula ...
d = √((x2 -x1)² +(y2 -y1)²)
The length of segment XY is ...
d = √((3 -(-1))² +(0 -3)²) = √(4² +(-3)²) = √25 = 5
The length of segment YZ is ...
d = √((-1 -3)² +(-2-0)²) = √((-4)² +(-2)²) = √20 ≈ 4.47
Sum of side lengths
Side XZ has length (3 -(-2)) = 5, the difference of y-coordinates. Then the perimeter is ...
P = XZ +XY +YZ = 5 +5 +4.47
P = 14.47 . . . . units
The perimeter of the triangle is about 14.47 units.
