Recall that a translation of n units to the left transforms the point (x,y) as follows:
[tex](x,y)\rightarrow(x-n,y).[/tex]
A vertical translation of n units up transforms the point as follows:
[tex](x,y)\rightarrow(x,y+n).[/tex]
Therefore, a point (x,y) translated 5 units to the left, and 3 units up is transformed as follows:
[tex](x,y)\rightarrow(x-5,y+3).[/tex]
Now, the coordinates of point P are:
[tex]P(3,-4),[/tex]
therefore, the image of point P under the transformations is:
[tex]P^{\prime}(3-5,-4+3)=P^{\prime}(-2,-1).[/tex]
Answer:
