Question

1. determine whether a translation maps quadrilateral lmnp onto quadrilateral ( lmnp ). if so, find the translation vector. if not, explain why.

Explanation:

Step1: Check the translation of point \(P\)

Assume the coordinates of \(P\) is \((x_1,y_1)\) and \(P'\) is \((x_2,y_2)\). Count the horizontal and vertical shifts.
If \(P\) moves to \(P'\), the horizontal shift \(a=x_2 - x_1\), vertical shift \(b=y_2 - y_1\).
From the graph, assume \(P=(1,4)\) and \(P'=(- 3,1)\). The horizontal shift \(a=-3 - 1=-4\), vertical shift \(b = 1 - 4=-3\).

Step2: Check the translation of point \(L\)

Assume \(L=(6,2)\). After translation \((x,y)\to(x - 4,y - 3)\), the image of \(L\) is \((6-4,2 - 3)=(2,-1)\) which is \(L'\) on the graph.

Step3: Check the translation of point \(M\)

Assume \(M=(7,0)\). After translation \((x,y)\to(x - 4,y - 3)\), the image of \(M\) is \((7-4,0 - 3)=(3,-3)\) which is \(M'\) on the graph.

Step4: Check the translation of point \(N\)

Assume \(N=(0,0)\). After translation \((x,y)\to(x - 4,y - 3)\), the image of \(N\) is \((0-4,0 - 3)=(-4,-3)\) which is \(N'\) on the graph.

Answer:

Yes, a translation maps quadrilateral \(LMNP\) onto \(L'M'N'P'\). The translation vector is \((-4,-3)\)