Question

Which of the following is the correct algebraic representation for a translation 5 units left and 2 units up?

a) (x+5, y+2)
b) (x+5, y-2)
c) (x-5, y+2)
d) (x-5, y-2)

Answer 1

The correct algebraic representation for a translation 5 units left and 2 units up is (x-5, y+2).

Step-by-step explanation:

The correct algebraic representation for a translation 5 units left and 2 units up is option c) (x-5, y+2). When translating a point horizontally, we change the x-coordinate by adding or subtracting the desired number of units. Since we are moving 5 units to the left, the x-coordinate should be subtracted by 5, which is represented by (x-5). Similarly, when translating a point vertically, we change the y-coordinate by adding or subtracting the desired number of units. Since we are moving 2 units up, the y-coordinate should be added by 2, which is represented by (y+2).