Question

The coordinates of triangle EFG are E(28, 24), F(24, 27), and G(0, 24).

a. What is the perimeter of triangle EFG? Round to the nearest tenth
b. Is the triangle equilateral, isosceles, or
scalene?

Answer 1

Higher Order Thinking There are points on a grid at (0, 0) and (3, 0).

a. What is a possible coordinate of the third vertex if the triangle has

a perimeter of 11 units? Explain.

b. Is there another point that could be the third vertex? Explain.

par poib

signe

Answer 2

a. 57.2

b. scalene

Explanation:

The lengths of the sides can be found from the coordinates of the vertices using the distance formula. The perimeter of the triangle is the sum of the side lengths.

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a.

The distance formula is ...

d = √((x2 -x1)² +(y2 -y1)²)

sides

The length of EF is ...

d = √((24 -28)² +(27 -24)²) = √(16 +9) = √25 = 5

The length of FG is ...

d = √((0 -24)² +(24 -27)²) = √(576 +9) = √585 ≈ 24.2

The points E and G lie on the same horizontal line, so the distance between them is the difference of their x-coordinates:

d = 28 -0 = 28 . . . . length of EG

perimeter

The perimeter is the sum of side lengths:

P = EF +FG +GE

P = 5 +24.2 +28 = 57.2

The perimeter of the figure is about 57.2 units.

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b.

The three sides have three different lengths. This makes the triangle a scalene triangle.