Question

The location of a point moved from 1, -3 to -2, -1 by translation. find the translation rule.

Answer 1

We have a point at (1,-3) and after a translation it is located at (-2,-1).

We can find the translation as the difference between the coordinates.

The rule for a translation is:

`(x,y)\to(x^(\prime),y^(\prime))=(x+a,y+b)`

Here we have:

`\begin{gathered} (x,y)=(1,-3) \\ (x^(\prime),y^(\prime))=(-2,-1)=(1+a,-3+b) \end{gathered}`

Then, we can find a and b as:

`\begin{gathered} -2=1+a\longrightarrow a=-2-1=-3 \\ -1=-3+b\longrightarrow b=-1+3=2 \end{gathered}`

Answer: The translation is T(-3,2). That is 3 units to the left and 2 units up.