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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.
FD
EF
DE (correct)

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

<p>52.8 (A)</p> Signup and view all the answers

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

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

Flashcards

Distance Formula

The distance between two points in a coordinate plane.

Perimeter of a triangle

The total length of all sides of a triangle added together.

Triangle

A three-sided closed figure.

Coordinates of a point

The specific locations of points on a coordinate plane, expressed as ordered pairs (x, y).

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Distance formula

A formula used to calculate the distance between two points in a coordinate plane. It uses the differences in the x and y coordinates.

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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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