contestada

Triangle DEF is dilated with respect to the origin by a scale factor of to produce AD'E'F. What is the length of side D'E"?
OA. 5 units
OB.
√3 units
O c.
√5 units
O D. 3√5 units
-8 -6
-4
-2
D₁
04
6
4
2-
-2
+4
+6
-0-
2
E
4
6
8
Xp

Triangle DEF is dilated with respect to the origin by a scale factor of to produce ADEF What is the length of side DE OA 5 units OB 3 units O c 5 units O D 35 u class=

Respuesta :

Answer:  [tex]\sqrt{5}[/tex] which is choice C

Explanation

Focus on points D(0,9) and E(3,3)

Take 1/3 of each coordinate to get D'(0,3) and E'(1,1)

Let's find the distance between those two new points.

[tex](x_1,y_1) = (0,3) \text{ and } (x_2, y_2) = (1,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-1)^2 + (3-1)^2}\\\\d = \sqrt{(-1)^2 + (2)^2}\\\\d = \sqrt{1 + 4}\\\\d = \sqrt{5}\\\\d \approx 2.2361\\\\[/tex]

Segment D'E' is exactly [tex]\sqrt{5}[/tex] units long which approximates to about 2.2361 units.

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