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www.ck12.org Chapter 1. Unit 1: Transformations, Congruence and Similarity
Guidance
In geometry, a transformation is an operation that moves, flips, or changes a shape (called the preimage) to create a
new shape (called the image). A translation is a type of transformation that moves each point in a figure the same
distance in the same direction. Translations are often referred to as slides. You can describe a translation using words
like "moved up 3 and over 5 to the left" or with notation. There are two types of notation to know.
1. One notation looks like T(3,5). This notation tells you to add 3 to the x values and add 5 to the y values.
2. The second notation is a mapping rule of the form (x,y) → (x −7,y +5). This notation tells you that the x and
y coordinates are translated to x −7 and y +5.
The mapping rule notation is the most common.
Example A
Sarah describes a translation as point P moving from P(−2,2) to P′(1,−1). Write the mapping rule to describe this
translation for Sarah.
Solution: In general ,P(x,y) → P′(x +a,y +b).
In this case, P(−2,2) → P′(−2+a,2+b) or P(−2,2) → P′(1,−1)
Therefore:
−2+a = 1 and 2+b = −1
a = 3 b = −3
The rule is:
(x,y) → (x +3,y −3)Answer:
Step-by-step explanation: