Question
How do you represent a translation algebraically? Select one: a. \( (-x,-y) \) b. \( (x+a, y+b) \) c. \( (-y,-x) \) d. \( (a x, b y) \)
Ask by Harper Fitzgerald. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct algebraic representation of a translation is \( (x + a, y + b) \).
Solution
To represent a translation algebraically, we need to understand that a translation involves shifting a point in the coordinate plane by a certain amount in the x-direction and y-direction.
The correct representation of a translation of a point \((x, y)\) by \(a\) units in the x-direction and \(b\) units in the y-direction is given by:
\[
(x + a, y + b)
\]
This means that you add \(a\) to the x-coordinate and \(b\) to the y-coordinate.
Thus, the correct answer is:
**b. \( (x+a, y+b) \)**
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Simplify this solution The Deep Dive
To represent a translation algebraically, you add a constant value to the x-coordinate and the y-coordinate of a point. This is expressed as \( (x+a, y+b) \), where \( a \) and \( b \) indicate how much the point is moved in the x-direction and y-direction respectively. This lovely formula ensures that every point moves precisely where you want it to go! In practical terms, if you have a point like \( (2, 3) \) and you want to translate it by \( 4 \) units right and \( 2 \) units up, you simply plug in the values: \( (2+4, 3+2) = (6, 5) \). Just like magic, you've found the new location!
