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

The answer is B: (,)

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

The answer is B: (,)