QUESTION IMAGE
Question
ions and perform the following rotations.
b. rotate triangle abc 180° clockwise about the origin.
c. rotate triangle abc 270° clockwise about the origin.
Part b: Rotate Triangle \( ABC \) \( 180^\circ \) clockwise about the origin
Step 1: Identify coordinates of \( A \), \( B \), \( C \)
From the graph (left):
- \( A(-5, 3) \)
- \( B(-2, 1) \)
- \( C(-5, 1) \)
Step 2: Apply \( 180^\circ \) rotation rule
The rule for a \( 180^\circ \) clockwise (or counterclockwise) rotation about the origin is \( (x, y) \to (-x, -y) \).
- For \( A(-5, 3) \):
\( (-(-5), -3) = (5, -3) \)
- For \( B(-2, 1) \):
\( (-(-2), -1) = (2, -1) \)
- For \( C(-5, 1) \):
\( (-(-5), -1) = (5, -1) \)
Part c: Rotate Triangle \( ABC \) \( 270^\circ \) clockwise about the origin
Step 1: Identify coordinates of \( A \), \( B \), \( C \)
From the graph (right):
- \( A(-5, 3) \)
- \( B(-2, 1) \)
- \( C(-5, 1) \)
Step 2: Apply \( 270^\circ \) clockwise rotation rule
The rule for a \( 270^\circ \) clockwise rotation about the origin is \( (x, y) \to (y, -x) \).
- For \( A(-5, 3) \):
\( (3, -(-5)) = (3, 5) \)
- For \( B(-2, 1) \):
\( (1, -(-2)) = (1, 2) \)
- For \( C(-5, 1) \):
\( (1, -(-5)) = (1, 5) \)
Final Rotated Coordinates
- Part b (\( 180^\circ \) clockwise):
\( A'(5, -3) \), \( B'(2, -1) \), \( C'(5, -1) \)
- Part c (\( 270^\circ \) clockwise):
\( A'(3, 5) \), \( B'(1, 2) \), \( C'(1, 5) \)
To graph the rotated triangles, plot these new coordinates and connect the vertices.
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Part b: Rotate Triangle \( ABC \) \( 180^\circ \) clockwise about the origin
Step 1: Identify coordinates of \( A \), \( B \), \( C \)
From the graph (left):
- \( A(-5, 3) \)
- \( B(-2, 1) \)
- \( C(-5, 1) \)
Step 2: Apply \( 180^\circ \) rotation rule
The rule for a \( 180^\circ \) clockwise (or counterclockwise) rotation about the origin is \( (x, y) \to (-x, -y) \).
- For \( A(-5, 3) \):
\( (-(-5), -3) = (5, -3) \)
- For \( B(-2, 1) \):
\( (-(-2), -1) = (2, -1) \)
- For \( C(-5, 1) \):
\( (-(-5), -1) = (5, -1) \)
Part c: Rotate Triangle \( ABC \) \( 270^\circ \) clockwise about the origin
Step 1: Identify coordinates of \( A \), \( B \), \( C \)
From the graph (right):
- \( A(-5, 3) \)
- \( B(-2, 1) \)
- \( C(-5, 1) \)
Step 2: Apply \( 270^\circ \) clockwise rotation rule
The rule for a \( 270^\circ \) clockwise rotation about the origin is \( (x, y) \to (y, -x) \).
- For \( A(-5, 3) \):
\( (3, -(-5)) = (3, 5) \)
- For \( B(-2, 1) \):
\( (1, -(-2)) = (1, 2) \)
- For \( C(-5, 1) \):
\( (1, -(-5)) = (1, 5) \)
Final Rotated Coordinates
- Part b (\( 180^\circ \) clockwise):
\( A'(5, -3) \), \( B'(2, -1) \), \( C'(5, -1) \)
- Part c (\( 270^\circ \) clockwise):
\( A'(3, 5) \), \( B'(1, 2) \), \( C'(1, 5) \)
To graph the rotated triangles, plot these new coordinates and connect the vertices.