The point A(-2, 3) is translated using T: (x,y) → (x + 4, y + 2).

What is the distance from A to A'?

a.) sqrt 6
b.) 2 sqrt2
c.)5
d.) 2 sqrt 5

Question

The point A(-2, 3) is translated using T: (x,y) → (x + 4, y + 2).

What is the distance from A to A'?

a.) sqrt 6
b.) 2 sqrt2
c.)5
d.) 2 sqrt 5

anonymous · Answer

@mathslover

anonymous · Answer

@mathhelp3

imstuck · Answer

The prompt x + 4 tell us to move the point 4 units to the right (in a positive direction) and up to (y is also moving in a positive direction).  A' is now located at (2, 5).  To find the distance between A and A', you will need the distance formula which is $$d=\sqrt{(x _{1}-x _{2})^{2}+(y _{1}-y _{2})^{2}}$$.  Plugging the values into the formula we get the square root of 20.  Depending upon how you need to answer it, decimal form is 4.472, or leaving the radical sign in the answer it is 2 times the square root of 5.

mathslover · Answer

The second coordinate will become : 

A' $\equiv (-2 + 4 , 3 + 2)$ 

or 

$A' \equiv (2,5) $ 

The rest is explained by @IMStuck very nicely.

anonymous · Answer

@IMStuck so the answer is 2 sqrt 5?

imstuck · Answer

Yes.  2square root 5 is the distance between A and A'.  Did you get that as well?

anonymous · Answer

yes I did thanks!

imstuck · Answer

Not a problem at all!  Glad to help!