Question

2.7 geometric transformations with refle
which statement correctly identifies the line of reflection?
the triangles are reflected across the x - axis.
the triangles are reflected across the line ( y = -x ).
the triangles are reflected across the line ( y = x ).
the triangles are reflected across the y - axis.

Explanation:

Step1: Identify key point coordinates

Take point $A(-5, 6)$ and its image $A'(5, 6)$; point $B(-4, 2)$ and its image $B'(4, 2)$.

Step2: Analyze reflection rule

For a point $(x,y)$, reflecting over the y-axis gives $( -x,y)$. Here, $(-5,6)\to(5,6)$ and $(-4,2)\to(4,2)$, which matches this rule.

Step3: Eliminate other options

• Reflecting over x-axis would give $(x,-y)$, which does not match the points.
• Reflecting over $y=-x$ would give $(-y,-x)$, which does not match.
• Reflecting over $y=x$ would give $(y,x)$, which does not match.

Answer:

The triangles are reflected across the y-axis.