Question

which figure shows a reflection of figure k across the y - axis? figure l figure m figure n

Explanation:

Step1: Understand the rule of reflection across y - axis

When a point \((x,y)\) is reflected across the \(y\) - axis, the new point is \((-x,y)\). In terms of a figure, each point of the original figure \(K\) will have its \(x\) - coordinate negated while the \(y\) - coordinate remains the same.

Step2: Analyze Figure \(L\)

For each vertex of Figure \(K\), if we change the sign of the \(x\) - coordinate (since reflection across \(y\) - axis: \((x,y)\to(-x,y)\)), we get the vertices of Figure \(L\). For example, if a vertex of \(K\) is \((- 3,4)\), after reflection across the \(y\) - axis, it becomes \((3,4)\) which is a vertex of Figure \(L\).

Step3: Analyze Figure \(M\)

Figure \(M\) is a reflection of Figure \(K\) across the \(x\) - axis (because for reflection across \(x\) - axis \((x,y)\to(x, - y)\)). If a vertex of \(K\) is \((-3,4)\), a vertex of \(M\) is \((-3,-4)\)

Step4: Analyze Figure \(N\)

Figure \(N\) is a reflection of Figure \(K\) across both the \(x\) - axis and \(y\) - axis. If a vertex of \(K\) is \((-3,4)\), a vertex of \(N\) is \((3,-4)\)

Answer:

Figure \(L\)