Question

1. what is the result after rotating a right triangle 90 degrees counterclockwise about the origin? the triangle preserves its shape but changes its orientation the triangle disappears the triangle changes its shape the triangle doubles its size

Explanation:

Rotation is a type of transformation in geometry. When a figure is rotated, it is turned around a fixed point (in this case, the origin). The key properties of rotation are that it is a rigid transformation. A rigid transformation preserves the shape and size of the figure. However, the orientation (the way the figure is positioned in space) changes. For example, if a right - triangle has its right - angle vertex at a certain position relative to the axes before rotation, after a 90 - degree counter - clockwise rotation, the positions of its vertices relative to the axes will be different (orientation change), but the lengths of its sides (so shape) and the measures of its angles (so it's still a right - triangle) remain the same.

• The option "The triangle disappears" is incorrect because rotation is a transformation that acts on the existing figure, not a deletion operation.
• The option "The triangle changes its shape" is wrong as rotation is a rigid transformation (preserves side lengths and angle measures).
• The option "The triangle doubles its size" is incorrect because rotation does not involve dilation (a transformation that changes the size).

Answer:

The triangle preserves its shape but changes its orientation.