Question

the graph shows quadrilaterals rstu and vwxy. is rstu similar to vwxy? justify your answer. yes, because a rotation 90° clockwise around the origin maps rstu onto vwxy yes, because a reflection over the x - axis maps rstu onto vwxy

Explanation:

Step1: Analyze rotation

A \(90^{\circ}\) clockwise rotation around the origin has the transformation rule \((x,y)\to(y, -x)\). For example, if \(U=(2,5)\), after \(90^{\circ}\) clockwise rotation around the origin, it should be \((5,- 2)\), but in \(VWXY\) there is no such point.

Step2: Analyze reflection

A reflection over the \(x -\)axis has the transformation rule \((x,y)\to(x,-y)\).
For \(U(2,5)\), after reflection over the \(x -\)axis, we get \((2,-5)\) which is \(Y\) point.
For \(R(3,9)\), after reflection over the \(x -\)axis, we get \((3,-9)\) which is \(V\) point.
For \(S(7,4)\), after reflection over the \(x -\)axis, we get \((7,-4)\) which is \(W\) point.
For \(T(5,0)\), after reflection over the \(x -\)axis, we get \((5,0)\) which is \(X\) point.

Answer:

Yes, because a reflection over the \(x -\)axis maps \(RSTU\) onto \(VWXY\)