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
A(-2,3),A'(x,y).
x+4 = -2+4 = 2.
y+2 = 3+2 = 5.
A(-2,3),A'(2,5).
D^2 = (2-(-2))^2 + (5-3)^2 = 20,
D = sqrt(20) = sqrt(4*5) = 2*sqrt5.
To find the distance between point A(-2, 3) and the translated point A', we can use the distance formula.
The distance formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Let's substitute the coordinates of A and A' into the formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-2 + 4)² + (3 + 2)²]
= √[2² + 5²]
= √[4 + 25]
= √29
Therefore, the distance from A to A' is √29.
To find the distance from point A (-2, 3) to its translated point A', we use the distance formula. The distance formula calculates the distance between two points (x1, y1) and (x2, y2) in a Cartesian plane.
The distance, d, between two points (x1, y1) and (x2, y2) is given by the formula:
d = square root((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point A' after translation are (x1 + 4, y1 + 2), which gives us point A' (2, 5). Using the formula, we can plug in the values:
d = square root((2 - (-2))^2 + (5 - 3)^2)
= square root((4)^2 + (2)^2)
= square root(16 + 4)
= square root(20)
Simplifying the square root of 20, we can write it as:
d = square root(4 * 5)
= square root(4) * square root(5)
= 2 * square root(5)
Therefore, the distance from A to A' is 2 * square root(5).