Question

Please help i am very confused

Which translation will change figure ABC to figure A'B'C'?

A coordinate plane is shown. Figure ABC is composed of coordinates A, negative 4 comma negative 1, B, negative 1 comma negative 1, C, and negative 2 comma negative 3. Figure A prime, B prime, and C prime is composed of coordinates A prime, 0 comma 2, B prime, 3 comma 2, C prime, 2 comma 0.

Answer 1

You can try graphing the coordinates and seeing if it is a translation, dilation, rotation, or reflection

Answer 2

The transformation is the function
`T : \mathbb{R}^2 \rightarrow \mathbb{R}^2` such that
`T(x,y)=(x+4,y+3)`, that is, a translation of 4 units right and 3 units up.

Explanation:

Notice that if you sum 4 to the first coordinate of the vertices of figure ABC, you will get the first coordinates of figure A'B'C', and if you do the same with second coordinates, but if you sum 3 to them, you will get the second coordinates of figure A'B'C', then, the transformation you are looking for is the one that sums 4 to the first coordinate and 3 to the second coordinate of every point of
`\mathbb{R}^2`.

Then, define a function
`T : \mathbb{R}^2 \rightarrow \mathbb{R}^2`, such that
`T(x,y)=(x+4,y+3)`, and that is your translation.