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
To find the distance from point A to its translated point, A', we'll first need to find the coordinates of A' by applying the translation.
The translation T: (x, y) → (x + 4, y + 2) means that we add 4 to the x-coordinate and 2 to the y-coordinate of the point.
So let's apply the translation to point A(-2, 3):
A' = (-2 + 4, 3 + 2)
= (2, 5)
Now that we have the coordinates of A' as (2, 5), we can find the distance between A and A' using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of A (-2, 3) and A' (2, 5):
Distance = √[(2 - (-2))^2 + (5 - 3)^2]
= √[(4)^2 + (2)^2]
= √[16 + 4]
= √20
Simplifying the square root:
Distance = √(4 * 5)
= √4 * √5
= 2 * √5
So the distance from A to A' is 2√5.