Question

1. reflection across the y - axis

a)
b)
c)
d)
c
b
d
a

Explanation:

To determine the reflection across the \( y \)-axis, we use the rule for reflecting a point \((x,y)\) across the \( y \)-axis: the new coordinates become \((-x,y)\). Let's analyze the original triangle's vertices. Suppose the original vertices (let's assume the top base vertices are \( J \) and \( W \), and the bottom vertex is \( U \)) have coordinates (for example, if \( J \) is at \((1,2)\), \( W \) at \((3,2)\), \( U \) at \((2,-1)\)). Reflecting across the \( y \)-axis, \( J(1,2) \) becomes \((-1,2)\), \( W(3,2) \) becomes \((-3,2)\), \( U(2,-1) \) becomes \((-2,-1)\). Now let's check the options:

• Option A: The vertices seem to be a reflection but maybe not across \( y \)-axis (orientation or coordinates don't match the \( y \)-axis reflection rule).
• Option B: The triangle is oriented differently (flipped vertically maybe), not a \( y \)-axis reflection.
• Option C: Let's check coordinates. If the original triangle is on the right of \( y \)-axis, reflecting to the left, the vertices of option C should match the \( (-x,y) \) transformation. For example, if original \( J \) is \( (1,2) \), reflected is \( (-1,2) \), \( W(3,2) \) reflected is \( (-3,2) \), \( U(2,-1) \) reflected is \( (-2,-1) \). Looking at option C's graph, the triangle is on the left of \( y \)-axis with vertices matching the reflection of the original (top base on left, bottom vertex on left).
• Option D: The triangle is distorted or not a reflection across \( y \)-axis.

So option C follows the reflection across \( y \)-axis rule (changing \( x \)-coordinates' sign, \( y \)-coordinates same).

Answer:

C