Question

the diagram shows the preimage abcd and five reflected images. match each reflection of abcd with its image after the transformation. drag the items on the left to the correct location on the right. across the origin (0,0) across the x - axis across the y - axis across the line y = x across the line y = - x

Explanation:

Step1: Reflection across the origin \((0,0)\)

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

Step2: Reflection across the \(x -\)axis

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

Step3: Reflection across the \(y -\)axis

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

Step4: Reflection across the line \(y = x\)

When a point \((x,y)\) is reflected across the line \(y=x\), the transformation rule is \((x,y)\to(y,x)\).

Step5: Reflection across the line \(y=-x\)

When a point \((x,y)\) is reflected across the line \(y =-x\), the transformation rule is \((x,y)\to(-y,-x)\).

Answer:

• across the origin \((0,0)\): The image in the third - quadrant (lower - left part of the coordinate system).
• across the \(x -\)axis: The image directly below the pre - image \(ABCD\) (in the fourth - quadrant).
• across the \(y -\)axis: The image to the left of the \(y -\)axis (in the second - quadrant).
• across the line \(y = x\): The image in the first - quadrant (upper - right part of the coordinate system).
• across the line \(y=-x\): The image in the fourth - quadrant (lower - right part of the coordinate system).