Respuesta :

The transformation is:
T : ( x , y ) → ( x + 2, y + 1 )
B ( 1, 3 ) → B` ( 1 + 2, 3 + 1 )
B ` ( 3, 4 )
d ( B B`) = √(( 3 - 1 )² + ( 4 - 3 )² )=
=  √ (2² + 1²) = √ 5

Answer:

[tex]\sqrt{5}\ units[/tex]


Step-by-step explanation:

we know that

The rule of the translation is equal to

[tex](x,y)-----> (x+2,y+1)[/tex]

That means

The translations is [tex]2[/tex] units to the right and [tex]1[/tex] unit up

Let

[tex](x,y)[/tex]-------> the coordinates of point B

[tex](x+2,y+1)[/tex]------> the coordinates of point B'

Find the distance

the formula to calculate the distance between two points is equal to


[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]


substitute

[tex]d=\sqrt{((y+1)-y)^{2}+((x+2)-x)^{2}}[/tex]


[tex]d=\sqrt{(1)^{2}+(2)^{2}}[/tex]


[tex]d=\sqrt{5}\ units[/tex]