Find the perimeter of the triangle with the coordinates (1, 1), (2, 2), and (3, 1).

Question

Find the perimeter of the triangle with the coordinates (1, 1), (2, 2), and (3, 1).

Answer 1

You must determine the length of each of the three line segments and add them.

Each segment can be determined using pythagorean theorem a^2 + b^2 = c^2 for a right triangle.

 

p1 = (1,1); p2 = (2,2)

rise = (y2-y1) = (2-1) = 1 = a

run = (x2-x1) = (2-1) = 1 = b

solve for hypotenuse of right triangle

1^2 + 1^2 = c^2 = 2

c = sqrt(2) = 1.414

 

p2 = (2,2); p3 = (3,1)

rise = (y3-y2) = (1-2) = -1 = a

run = (x3-x2) = (3-1) = 1 = a

(-1)^2 + 1^2 = 2 = c^2

c = sqrt(2) = 1.414

 

p3 = (3,1); p1 = (1,1)

rise = (y1-y3) = 1-3 = -2

run = (x1-x3) = 1-1 = 0

(-2)^2 + 0^2 = 4 = c^2

c = sqrt(4) = 2

=

Now add all three segments, such that the perimeter is equal to 2 + 2[sqrt(2)] = 2 + 2(1.414) = 4.848