Question

which is the image of triangle e after a reflection over the y - axis?
a. triangle a
b. triangle b
c. triangle c
d. triangle d

Explanation:

To determine the image of triangle \( E \) after a reflection over the \( y \)-axis, we use the rule for reflecting a point \((x, y)\) over the \( y \)-axis: the \( x \)-coordinate changes sign, while the \( y \)-coordinate remains the same, i.e., \((x, y) \to (-x, y)\).

Looking at the positions of the triangles:

• Triangle \( E \) is in the first quadrant (positive \( x \) and positive \( y \)).
• After reflecting over the \( y \)-axis, its image should be in the second quadrant (negative \( x \), positive \( y \)).
• Triangle \( A \) is in the second quadrant and has the same shape and orientation as \( E \) when reflected over the \( y \)-axis.
• Triangle \( B \) is in the third quadrant (negative \( x \), negative \( y \)), triangle \( C \) is in the first quadrant (positive \( x \), positive \( y \)) but oriented differently, and triangle \( D \) is in the fourth quadrant (positive \( x \), negative \( y \)), so they do not match the reflection of \( E \) over the \( y \)-axis.

Answer:

A. triangle A