Question

describe the transformation shown in the graph. rotate 270 degrees ccw reflect over y - axis reflect over x - axis rotate 90 degress ccw

Explanation:

Step1: Recall reflection over x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). This means the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign.

Step2: Analyze the graph

Looking at the two triangles (original and transformed) in the graph, we can observe that for each corresponding vertex of the two triangles, the \(x\) - coordinate is unchanged and the \(y\) - coordinate is the negative of the original. For example, if a vertex of the original triangle is \((a,b)\), the corresponding vertex of the transformed triangle is \((a, - b)\). This is consistent with the rule of reflection over the \(x\) - axis.

Step3: Eliminate other options

• Rotate 270 degrees CCW: The rule for rotating a point \((x,y)\) 270 degrees counter - clockwise is \((x,y)\to(y, - x)\). This would change both the \(x\) and \(y\) coordinates in a non - sign - change (for \(y\)) way (in a more complex coordinate swap), which is not what we see in the graph.
• Reflect over y - axis: The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). But in our graph, the \(x\) - coordinate of corresponding vertices does not change sign.
• Rotate 90 degrees CCW: The rule for rotating a point \((x,y)\) 90 degrees counter - clockwise is \((x,y)\to(-y,x)\). This also changes the coordinates in a more complex swap (not just a sign change for \(y\)) which is not in line with the graph.

Answer:

Reflect over x - axis