Question

Which of the following rules would translate ΔABC
5 units left and 3 units up?

Option #1: (x,y)→(x−5,y+3)


Option #2: (x,y)→(5x,3y)


Option #3: (x,y)→(x+3,y−5)

Answer 1

To translate \(\Delta ABC\) 5 units left and 3 units up, you want to adjust the x-coordinate and y-coordinate of each point as follows:

- Moving 5 units left means you subtract 5 from the x-coordinate.
- Moving 3 units up means you add 3 to the y-coordinate.

Based on this, the correct transformation would be:

\[
(x, y) \rightarrow (x - 5, y + 3)
\]

Now let's evaluate the options:

- **Option #1**: \((x,y) \rightarrow (x - 5, y + 3)\) is correct.

- **Option #2**: \((x,y) \rightarrow (5x, 3y)\) does not represent a translation but rather a scaling transformation, which is not what we want.

- **Option #3**: \((x,y) \rightarrow (x + 3, y - 5)\) would move a point 3 units to the right (not left) and 5 units down (not up), which is also not correct.

Therefore, the correct answer is **Option #1**: \((x,y) \rightarrow (x - 5, y + 3)\).