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Geometry Quiz: Triangle DEF Properties

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Questions and Answers

What is the approximate length of side DE of triangle DEF?

19.21

17.46 (correct)

52.79

16.12

Which expression correctly calculates the length of side EF?

$\sqrt{(-7 - (-9))^2 + (-7 - 9)^2}$

$\sqrt{(8 - 9)^2 + (5 - 7)^2}$

$\sqrt{(8 - (-9))^2 + (5 - 9)^2}$

$\sqrt{(8 - (-7))^2 + (5 - (-7))^2}$ (correct)

If the coordinates of D were changed to (-8, 8) and all other coordinates were the same, which side's length would be most affected (increased or decreased) ?

All sides would be equally affected.

DE (correct)

What is the perimeter of triangle DEF, rounded to the nearest tenth?

<p>52.8</p> Signup and view all the answers

What is the distance between points F and D calculated as?

<p>$\sqrt{(2)^2 + (-16)^2}$</p> Signup and view all the answers

Study Notes

Coordinates of the vertices

D(-9, 9)
E(8, 5)
F(-7, -7)

Calculating the lengths of the sides

DE: √[(8 - (-9))² + (5 - 9)²] = √(17² + (-4)²) = √289 + 16 = √305 ≈ 17.46
EF: √[(8 - (-7))² + (5 - (-7))²] = √(15² + 12²) = √225 + 144 = √369 ≈ 19.21
FD: √[(-7 - (-9))² + (-7 - 9)²] =√(2² + (-16)²) =√4 + 256 =√260 ≈ 16.12

Perimeter of ΔDEF

Perimeter = DE + EF + FD = 17.46 + 19.21 + 16.12 ≈ 52.79
Perimeter ≈ 52.8 units

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Description

Test your understanding of the properties of triangle DEF by calculating the lengths of its sides and determining the perimeter. This quiz covers the application of the distance formula in coordinate geometry. Perfect for students studying geometry concepts in a classroom setting.