The point A(-2, 3) is translated using T: (x,y) → (x + 4, y + 2).
What is the distance from A to A'?
square root 6
2 square root 2
5
2 square root 5
well, (-2,3) --> (2,5)
now find the distance as usual.
To find the distance between two points, you can use the distance formula.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's denote the coordinates of A as (x1, y1) = (-2, 3).
Now we can apply the translation T: (x, y) → (x + 4, y + 2) to find the new coordinates of the translated point A'.
To perform the translation, we add the corresponding values:
x' = x + 4
y' = y + 2
For point A, we have:
x' = -2 + 4 = 2
y' = 3 + 2 = 5
So the coordinates of A' are (x2, y2) = (2, 5).
Now we can substitute the values into the distance formula:
d = sqrt((2 - (-2))^2 + (5 - 3)^2)
= sqrt((2 + 2)^2 + (5 - 3)^2)
= sqrt(4^2 + 2^2)
= sqrt(16 + 4)
= sqrt(20)
= 2 * sqrt(5)
Therefore, the distance from A to A' is 2 * sqrt(5).