Question

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
X

Answer 1

Answer:

C

Step-by-step explanation:

Since the dilatation is centred at the origin , then each of the original coordinates of points D and E are multiplied by the scale factor of $\frac{1}{3}$

D (0, 9 ) → D' ($\frac{1}{3}$ (0), $\frac{1}{3}$ (9) ) → D' (0, 3 )

E (3, 3 ) → E' ($\frac{1}{3}$ (3), $\frac{1}{3}$ (3) ) → (1, 1 )

to calculate the length of D'E' , use the distance formula

D'E' = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

let (x₁, y₁ ) = D' (0, 3 ) and (x₂, y₂ ) = E' (1, 1 )

substitute these values into the formula for D'E'

D'E' = $\sqrt{(1-0)^2+(1-3)^2}$

      = $\sqrt{1^2+(-2)^2}$

      = $\sqrt{1+4}$

      = $\sqrt{5}$