Question

Find the perimeter of a quadrilateral with vertices at G (1, 6), H (2.5, 4), I (1, 2), K (-0.5, 4). Round your answer to the nearest hundredth when necessary. (5 points) 5 units 12.5 units 7.5 units 10 units

Answer 1

The points form a rhombus, so the total perimeter is 4 times the length of one side. The difference in coordinates G and H is ...

... H - G = (2.5-1, 4-6) = (1.5, -2)

Then the length of GH can be found from the Pythagorean theorem to be

... GH = √(1.5² + (-2)²) = √(2.25+4) = √6.25

... GH = 2.5

The perimeter is 4 times that, so is 4×2.5 = 10 units.