Question

Which rule describes a translation that is 3 units to the right and 5 units down?

(x, y) (x − 3, y − 5)
(x, y) (x + 3, y − 5)
(x, y) (x + 3, y + 5)
(x, y) (x − 3, y + 5)

Answer 1

(x, y) (x + 3, y − 5)

Explanation:

A translation is a rigid transformation that changes the position of a graph to the right, left, up, or down.

Moving Right

The question states that the point is moving 3 units to the right. This is a horizontal transformation, which means it will affect the x-value.

When you move to the right on the x-axis, the number becomes greater. So to describe a translation of 3 to the right, add 3.

Moving Down

The next translation moves down, which is a vertical change. So, we are changing the y-value.

Numbers decrease as you move down the y-axis. This means to describe a translation down 5 units, subtract 5.

Writing a Translation

Now that we know our 2 translations, we can write them as a coordinate pair.

First, write the pair (x,y). Then write a coordinate pair using the translations, (x + 3, y − 5).