Nathan draws a triangle on the coordinate grid. He marks his points at (1,5)

Question

, (4,1)
, and (−4,−5)
. What is the perimeter of the triangle, rounded to the nearest tenth of a unit? Explain the steps that Nathan must take to find the solution.

Answer 1

To find the perimeter of a triangle, Nathan must first calculate the distance between each pair of points.

Using 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],

Nathan can find the distances between the points:

d₁ = √[(4 - 1)² + (1 - 5)²] = √[3² + (-4)²] = √(9 + 16) = √25 = 5 units,

d₂ = √[(-4 - 1)² + (-5 - 1)²] = √[(-5)² + (-6)²] = √(25 + 36) = √61 ≈ 7.81 units,

d₃ = √[(-4 - 1)² + (-5 - 5)²] = √[(-5)² + (-10)²] = √(25 + 100) = √125 ≈ 11.18 units.

Next, Nathan must add up the distances to find the perimeter:

Perimeter = d₁ + d₂ + d₃ = 5 + 7.81 + 11.18 = 23.99 ≈ 24 units.

Therefore, the perimeter of the triangle, rounded to the nearest tenth of a unit, is 24 units.