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? Explain the steps that Nathan must take to find the solution.
To find the perimeter of a triangle on a coordinate grid, Nathan must calculate the distance between each set of consecutive points, and then add up those distances.
First, Nathan can use the distance formula to find the distance between the points (1,5) and (4,1):
d1 = √[(4 - 1)^2 + (1 - 5)^2]
= √[3^2 + (-4)^2]
= √[9 + 16]
= √25
= 5
Next, Nathan can find the distance between the points (4,1) and (-4,-5):
d2 = √[(-4 - 4)^2 + (-5 - 1)^2]
= √[-8^2 + (-6)^2]
= √[64 + 36]
= √100
= 10
Finally, Nathan can find the distance between the points (-4,-5) and (1,5):
d3 = √[(1 - (-4))^2 + (5 - (-5))^2]
= √[5^2 + 10^2]
= √[25 + 100]
= √125
≈ 11.2
Now, Nathan can add up the distances to find the perimeter:
perimeter = d1 + d2 + d3
= 5 + 10 + 11.2
≈ 26.2
Therefore, the perimeter of the triangle is approximately 26.2 units.