Question

which of the following transformations, when applied to a triangle in the coordinate plane, will result in a congruent triangle? select all the correct answers.

• a reflection across the x - axis
• a translation 6 units to the left
• a rotation 90° clockwise about the origin
• a dilation centered at the origin with a scale factor of 3

Explanation:

1. Reflection across the x - axis: A reflection is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, a triangle reflected across the x - axis will have the same side lengths and angles as the original triangle, meaning it is congruent.
2. Translation 6 units to the left: A translation is also a rigid transformation. It only moves the figure without changing its shape or size. So, a triangle translated 6 units to the left will be congruent to the original triangle.
3. Rotation 90° clockwise about the origin: Rotation is a rigid transformation. It rotates the figure around a point (the origin in this case) without altering the side lengths or angles of the triangle. Thus, the rotated triangle is congruent to the original.
4. Dilation centered at the origin with a scale factor of 3: Dilation is a non - rigid transformation. It changes the size of the figure. A scale factor of 3 means the side lengths of the triangle will be multiplied by 3, so the resulting triangle is not congruent to the original.

Answer:

A. a reflection across the x - axis
B. a translation 6 units to the left
C. a rotation 90° clockwise about the origin