Respuesta :
Ok, so
Here we have this linear transformation as follows:
[tex]T\colon(x,y)=(x+4,y+2)[/tex]And we're going to translate the point A:
[tex]A(-2,3)[/tex]This is: (We replace the values of x and y of the point A in the transformation):
[tex]\begin{gathered} T\colon(-2,3)=(-2+4,3+2) \\ T\colon(-2,3)=(2,5) \end{gathered}[/tex]The point A translated will give us a new point B, which is (2 , 5) (After applying the transformation).
Now, let's find the distance between A (-2,3) and B (2,5).
Remember that the distance between two points:
[tex]\begin{gathered} A(x_1,y_1) \\ B(x_{2,}y_2) \end{gathered}[/tex]Can be found applying the following formula:
[tex]D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Replacing our values:
[tex]\begin{gathered} D=\sqrt[]{(5-3)^2+(2-(-2))^2} \\ D=\sqrt[]{(2)^2+(2+2)^2} \\ D=\sqrt[]{4+16} \\ D=\sqrt[]{20} \end{gathered}[/tex]Therefore, the distance between the points A and B, is √(20) units. (This is, approximately, 4.47)
