Math Practice Online > free > lessons > New York > 7th grade > Translations and Reflections

Here are some tips for Translations and Reflections, which aligns with New York state standards:

Translations and Reflections

For this topic, you will need to know ordered pairs.
To review the Ordered Pairs topic, see here.

Translations are changes by directions: up, down, left, and right.

Translation Change
h units to the right x changes to x + h
h units to the left x changes to x - h
h units up y changes to y + h
h units down y changes to y - h

Reflections are changes across the x-axis or the y-axis.

Reflection Change
over the y-axis x changes to -x
over the x-axis y changes to -y

Example 1: Translation

Enter the coordinates of each point as an ordered pair.
 B is a translation of A by 9 units to the right and 13 units upward. B: (,)

You find point B by translating point A by 9 units to the right and 13 units upwards.

 x-coordinate of point B = x-coordinate of point A + 9 = -6 + 9 = 3
 y-coordinate of point B = y-coordinate of point A + 13 = -5 + 13 = 8

Example 2: Translation and Reflection

Enter the coordinates of each point as an ordered pair.
 A is translated by 20 units to the left and 3 units downward. A is then reflected over the y-axis to get B. B: (,)

This problem involves translating and then reflecting point A to get point B.

Translation:

Point A is translated by 20 units to the left and 3 units downward.
 x-coordinate of translated point A = x-coordinate of point A - 20 = 13 - 20 = -7
 y-coordinate of translated point A = y-coordinate of point A - 3 = -5 - 3 = -8
The translated point A has coordinates (-7, -8).
Reflection:
To get point B, the translated point A is reflected over the y-axis.
This means that the y-coordinate stays the same but the x-coordinate changes.
 x-coordinate of point B = - (x-coordinate of translated point A) = - (-7) = 7
 y-coordinate of point B = y-coordinate of translated point A = - 8