Question

Nathan draws a triangle on the coordinate grid. He marks his points at (1,5)
, (4,1)
, and (−4,−5)
. What is the perimeter of the triangle, rounded to the nearest tenth of a unit? Show all steps that Nathan must take to find the solution.(4 points)

Answer 1

Step 1 — Label the points:
A = (1, 5), B = (4, 1), C = (−4, −5).

Step 2 — Use the distance formula d = sqrt((x2 − x1)^2 + (y2 − y1)^2) for each side.

AB:
dx = 4 − 1 = 3, dy = 1 − 5 = −4
AB = sqrt(3^2 + (−4)^2) = sqrt(9 + 16) = sqrt(25) = 5

BC:
dx = −4 − 4 = −8, dy = −5 − 1 = −6
BC = sqrt((−8)^2 + (−6)^2) = sqrt(64 + 36) = sqrt(100) = 10

CA:
dx = 1 − (−4) = 5, dy = 5 − (−5) = 10
CA = sqrt(5^2 + 10^2) = sqrt(25 + 100) = sqrt(125) = 5√5 ≈ 11.1803399

Step 3 — Add the side lengths to get the perimeter:
Perimeter = AB + BC + CA = 5 + 10 + 5√5 = 15 + 5√5 ≈ 26.1803399

Rounded to the nearest tenth: 26.2 units.