Question

The coordinates of the vertices of △HIJ are H(−2,2), I(8,−2), and J(−4,−3). Identify the perimeter of △HIJ to the nearest tenth

Answer 1

28.2

Explanation:

The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.

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graphing aid

The values computed by the graphing program in the attachment add up to 28.2 units.

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using algebra

The length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...

d = √(rise^2 +run^2)

HI = √((-4)^2 +10^2) = √116 ≈ 10.770

IJ = √(1^2 +12^2) = √145 ≈ 12.042

JH = √(5^2 +2^2) = √29 ≈ 5.385

The perimeter is the total of the lengths of the sides:

P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197

To the nearest tenth, the perimeter is 28.2 units.