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.(4 points)
To find the perimeter of a triangle, Nathan needs to calculate the total distance between the three points.
First, Nathan needs to find the distance between (1,5) and (4,1). Nathan can use the distance formula to find this distance:
√((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, the distance between (1,5) and (4,1) is:
√((4 - 1)^2 + (1 - 5)^2)
= √(3^2 + (-4)^2)
= √(9 + 16)
= √25
= 5 units
Next, Nathan needs to find the distance between (1,5) and (-4,-5). Using the distance formula again:
√((-4 - 1)^2 + (-5 - 5)^2)
= √((-5)^2 + (-10)^2)
= √(25 + 100)
= √125
= 11.2 units (rounded to the nearest tenth)
Finally, Nathan needs to find the distance between (-4,-5) and (4,1):
√((4 - (-4))^2 + (1 - (-5))^2)
= √((8)^2 + (6)^2)
= √(64 + 36)
= √100
= 10 units
To calculate the perimeter, Nathan needs to add up the three distances:
5 + 11.2 + 10 = 26.2 units
Therefore, the perimeter of the triangle, rounded to the nearest tenth, is 26.2 units.