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.