Question

Triangle DEF has vertices D (2, 4), E (3, 7), and F (6, 5). Triangle DEF was translated 3 units to the left and 2 units down to form triangle D'E'F'. a. What rule describes the translation applied to triangle DEF to

create triangle D'E'F'?

Answer 1

Answer:
`(\text{x}, \text{y}) \to (\text{x}-3, \text{y}-2)`

The jump from x to x-3 means "move 3 units left".

The jump from y to y-2 means "move 2 units down".

Let's look at an example. I'll apply that rule to move point D(2,4).

`(\text{x},\text{y})\to(\text{x}-3,\text{y}-2)\\\\(2,4)\to(2-3,4-2)\\\\(2,4)\to(-1,2)\\\\`

The preimage point D(2,4) moves to the image point D' (-1,2) after the movement pattern "3 left, 2 down". I recommend using a graphing tool like Desmos or GeoGebra to plot these points. I'll let the student use the transformation rule on points E and F.