Question

which graph best describes a shape that is reflected over the x - axis?

Explanation:

Step1: Recall the reflection rule over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).

Step2: Analyze each graph

• For the first graph (top - left), it does not follow the \(x\) - axis reflection rule as the vertical relationship (y - coordinate transformation) is not \(y\to - y\) for corresponding points.
• For the second graph (middle - left), if we consider a general point \((x,y)\) on one shape and its corresponding point on the other shape, we can see that for each point \((x,y)\) on one triangle, the other triangle has a point \((x, - y)\). For example, if we assume a vertex \((a,b)\) on one triangle, the corresponding vertex on the other triangle is \((a, - b)\) which is in line with the \(x\) - axis reflection rule \((x,y)\to(x, - y)\).
• For the third graph (bottom - left), the transformation is not a reflection over the \(x\) - axis. If we check the coordinates of corresponding points, they do not follow the \(y\to - y\) rule.
• For the fourth graph (bottom - right), the transformation is not a reflection over the \(x\) - axis. The relationship between the coordinates of corresponding points does not match the \(x\) - axis reflection rule.

Answer:

The second graph (the one with two triangles where for each point \((x,y)\) on one triangle, the other triangle has a point \((x, - y)\)) best describes a shape that is reflected over the \(x\) - axis.