Question

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

Answer 1

Answer:

Distance between A and A' is 2√5.

Step-by-step explanation:

The given point A is translated to A' by using T: (x, y) → (x + 4, y+2).

We have to calculate the distance from A and A'

if A is (-2, 3) then the translated point A' will be ( -2+4, 3+2)≅(2, 5)

Now we can calculate the distance between A and A' by using the distance formula

Distance = √[(-2-2)²+(3-5)²] = √(-4)²+(-2)² = √16+4 = √20

              = 2√5

So the correct answer is distance = 2√5.

Answer 2

For this case, we have that by definition, the distance between two points is given by:

$d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}$

We have to:

$A: (x_ {1}, y_ {1}) = (- 2,3)\\A ':( x_ {2}, y_ {2}) = (x + 4, y + 2) = (- 2 + 4, 3 + 2) = (2,5)$

Substituting:

$d = \sqrt {(2 - (- 2)) ^ 2+ (5-3) ^ 2}\\d = \sqrt {(4) ^ 2 + (2) ^ 2}\\d = \sqrt {16 + 4}\\d = \sqrt {20}$

Answer:

$d = \sqrt {20}$