Given a triangle with vertices A(2,3), B(4,5), and C(3,6), reflect it across: 1. The x-axis (Plot the new vertices A1, B1, and C1) 2. The y-axis (Plot the new vertices A2, B2, and C2) 3. The line y=x (Swap the x and y coordinates to find the new vertices A3, B3, and C3).
Answer (1)
To reflect a triangle across different lines, you will need to adjust the coordinates of the vertices according to specific reflection rules. Here's how to reflect the triangle with vertices A(2,3), B(4,5), and C(3,6) across different lines:
Reflect across the x-axis:
When you reflect a point across the x-axis, you change the sign of the y-coordinate while keeping the x-coordinate the same.
For vertex A(2,3), the new coordinates will be A 1 ( 2 , − 3 ) .
For vertex B(4,5), the new coordinates will be B 1 ( 4 , − 5 ) .
For vertex C(3,6), the new coordinates will be C 1 ( 3 , − 6 ) .
Reflect across the y-axis:
When you reflect a point across the y-axis, you change the sign of the x-coordinate while keeping the y-coordinate the same.
For vertex A(2,3), the new coordinates will be A 2 ( − 2 , 3 ) .
For vertex B(4,5), the new coordinates will be B 2 ( − 4 , 5 ) .
For vertex C(3,6), the new coordinates will be C 2 ( − 3 , 6 ) .
Reflect across the line y = x :
When you reflect a point across the line y = x , you swap the x-coordinate and y-coordinate positions.
For vertex A(2,3), the new coordinates will be A 3 ( 3 , 2 ) .
For vertex B(4,5), the new coordinates will be B 3 ( 5 , 4 ) .
For vertex C(3,6), the new coordinates will be C 3 ( 6 , 3 ) .
These transformations give you the coordinates of the reflected vertices, forming new triangles in each case. You can plot these points on a coordinate plane to visualize the reflections.
