algebra
(2,3), (2,-1), (-3,-1)
what is the length of side 1?
what is the length of side 2?
what is the length of side 3?
what is the perimeter of the triangle?
To find the length of a side of a triangle, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the length of each side:
Side 1: Length between (2, 3) and (2, -1)
d1 = √((2 - 2)^2 + (-1 - 3)^2) = √(0 + 16) = √16 = 4
Side 2: Length between (2, -1) and (-3, -1)
d2 = √((-3 - 2)^2 + (-1 - (-1))^2) = √((-5)^2 + 0^2) = √(25 + 0) = √25 = 5
Side 3: Length between (-3, -1) and (2, 3)
d3 = √((2 - (-3))^2 + (3 - (-1))^2) = √((2 + 3)^2 + (3 + 1)^2) = √(5^2 + 4^2) = √(25 + 16) = √41
Perimeter of the triangle is the sum of the lengths of all three sides:
Perimeter = d1 + d2 + d3 = 4 + 5 + √41 ≈ 9 + √41.