Math Problem Statement
A sequence of transformations is to be performed on ∆RST. The first part of the sequence of transformations is to rotate the triangle 90° counterclockwise about the point (0, 0).
What are the coordinates of R’,S' and T' ?
A sequence of transformations is to be performed on ∆RST. The first part of the sequence of transformations is to rotate the triangle 90° counterclockwise about the point (0, 0).
What are the coordinates of R’,S' and T' ?
R’(1, 2), S’(3, 5), and T’(7, 3)
R’(-1, -2), S’(-3,- 5), and T’(-7, -3)
R’(2,1), S’(5,3), and T’(3,7)
R’(-2,1), S’(-5,3), and T’-(3,7)
Solution
To solve this, let’s recall the rule for a 90° counterclockwise rotation about the origin, . When a point is rotated 90° counterclockwise, its coordinates transform as follows:
Using this rule, we’ll apply the transformation to each point in .
If the problem had provided initial coordinates of , , and , we would calculate the transformations directly. Since we only have options, we’ll apply the rotation rule to each given option to check which matches a 90° counterclockwise rotation.
Let's analyze each option:
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Option 1:
- Rotation does not match , so this is not the correct answer.
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Option 2:
- This represents a 180° rotation, not 90° counterclockwise, so this is not the correct answer.
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Option 3:
- This option shows the points in a format, not , so it’s incorrect.
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Option 4:
- This option shows points transformed by the rule , so Option 4 is correct.
Answer: The correct coordinates of , , and after a 90° counterclockwise rotation about are:
Would you like further details on transformation rules?
Related Questions:
- What is the rule for a 180° rotation around the origin?
- How would a 90° clockwise rotation change the coordinates?
- What would happen if we rotated by 270° counterclockwise?
- How do you determine rotation direction based on positive or negative angles?
- How are translations and rotations combined in a sequence of transformations?
Tip: For any 90° counterclockwise rotation, swap and and negate the new -coordinate: .
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Rotations
Transformations
Formulas
Rotation formula for 90° counterclockwise about the origin: (x, y) → (-y, x)
Theorems
Transformation of coordinates under rotation
Suitable Grade Level
Grades 9-10