Question

The point A(-2, 3) is translated using T: (x,y) → (x + 4, y + 2). What is the distance from A to A'?

Answer 1

4.47 units (rounded to 2 decimal places)

Explanation:

According to translation T, the points for A' would be:

(-2,3) ----------- (-2+4,3+2) = (2,5)

Hence,

A'(2,5) and A (-2,3)

We find the distance using distance formula:

`√((y_2-y_1)^2+(x_2-x_1)^2)`

Where

x1 = 2,

x2= -2

y1 = 5

y2 = 3

Putting these, we find the distance, D:

`D=√((y_2-y_1)^2+(x_2-x_1)^2) \\D=√((3-5)^2+(-2-2)^2) \\D=√((-2)^2 + (-4)^2) \\D=√(4+16) \\D=√(20)\\ D=4.47`

The distance is 4.47 units (rounded to 2 decimal places)