Question

is cdef similar to lmno? justify your answer.
yes, because a translation left 7 units and down 10 units maps cdef onto lmno.
yes, because a rotation 180° around the origin maps cdef onto lmno.
no, because ∠c and ∠l do not have the same measure.

Explanation:

Step1: Check translation

If we consider translation left \(7\) units and down \(10\) units:
For a point \((x,y)\) in \(CDEF\), the translated point would be \((x - 7,y-10)\).
Take point \(C\) (assume coordinates from the graph, say \(C=(4,9)\)), after translation \((4 - 7,9-10)=(-3,-1)\) which is \(L\)'s coordinate.
Take point \(D=(7,6)\), after translation \((7 - 7,6 - 10)=(0,-4)\) which is not \(M\)'s coordinate (\(M=(0,-5)\)). So translation is not correct.

Step2: Check rotation

For a \(180^{\circ}\) rotation around the origin, the transformation rule is \((x,y)\to(-x,-y)\).
If \(C=(4,9)\), after \(180^{\circ}\) rotation \((-4,-9)\) which is not \(L\)'s coordinate (\(L=(-3,-1)\)).

Step3: Check angle - side relationship

Similar polygons have corresponding angles equal. If we assume \(CDEF\) and \(LMNO\) are similar, their corresponding angles should be equal. But from the graph (by visual inspection or using slope to find angles), \(\angle C\) and \(\angle L\) do not have the same measure.

Answer:

No, because \(\angle C\) and \(\angle L\) do not have the same measure.