Question

Triangle abc is reflected across the line y=3x-1 to form triangle rst. Select all the true statements.

1) Triangle abc and triangle rst are congruent.
2) Triangle abc and triangle rst have the same area.
3) Triangle abc and triangle rst have the same perimeter.
4) Triangle abc and triangle rst have the same angles.

Answer 1

Triangle abc is reflected across the line y=3x-1 to form triangle rst.

1) False

2) True

3) False

4) True

Step-by-step explanation:

Triangle ABC and Triangle RST are not congruent because a reflection preserves shape but not necessarily size. The line of reflection, y = 3x - 1, acts as a mirror, so corresponding sides are equal, but the triangles may be of different sizes.

However, the two triangles have the same area. In a reflection, the area remains constant since it's based on the base and height, and these are unchanged by reflection. So, statement 2 is true.

The statement about the perimeter (statement 3) is false. Reflection preserves the lengths of individual sides, but it doesn't preserve the total perimeter since the arrangement of those sides changes.

Lastly, the statement about angles (statement 4) is true. Reflection preserves angles, so corresponding angles in both triangles are congruent.