Question

1. a reflection over which line will carry the isosceles triangle onto itself?

options: x - axis, y - axis, x = - 1, y = x

Explanation:

Step1: Recall Reflection Symmetry

For a figure to map onto itself via reflection, the line of reflection must be a line of symmetry. An isosceles triangle has a vertical line of symmetry (if oriented with the vertex at the top) that divides it into two congruent halves.

Step2: Analyze the Graph

The triangle is symmetric about the \( y \)-axis (the vertical line \( x = 0 \)). Reflecting over the \( y \)-axis will map each point \((x,y)\) to \((-x,y)\), which for this triangle, will map the left half to the right half and vice versa, carrying the triangle onto itself. Reflecting over \( x \)-axis would flip it vertically (not matching), \( x=-1 \) is not the axis of symmetry, and \( y = x \) would rotate/reflection not matching the triangle's symmetry.

Answer:

B. \( y \)-axis (assuming the options are labeled as: A. \( x \)-axis, B. \( y \)-axis, C. \( x = -1 \), D. \( y = x \))