Question

What is the rule for the transformation from triangle EFG to triangle E'F'G'?

Answer 1

Answer:

The rule of the transformation is 6 units up and 3 units to the right $T_{(3, \ 6)}$ and an horizontal dilation of 2 as well as a vertical dilation of 4.

Step-by-step explanation:

The given coordinates of EFG and E'F'G' from the chart are;

E(3, 2)

F(9, 5)

G(9, 2)

E'(6, 8)

F'(18, 20)

G'(18, 8)

Therefore, we have, given that the y-coordinates of E and G are the same, the length of segment EG = 9 - 3 = 6 units

Similarly, given that the x-coordinates of F and G are the same, the length of segment FG = 5 - 2 = 3 units

The length of segment FE =  $l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$ which gives;

Length from E(3, 2) to F(9, 5) = $l = \sqrt{\left (5-2 \right )^{2}+\left (9-3 \right )^{2}} = 3 \cdot \sqrt{5}$

For similarly oriented E'F'G', we have;

E'G' = 18 - 6 = 12

F'G' = 20 - 8 = 12

E'F' = 12·√2

Therefore, the transformation is 6 units up and 3 units to the right and an horizontal dilation of 2 as well as a vertical dilation of 4.