Question

find the coordinates of the vertices of the figure after the given transformation.
translation: $(x,y)\to(x + 1,y - 1)$
a $n(0,-2),f(4,2),q(4,-2)$
b $n(-1,1),f(3,-3),q(3,1)$
c $n(0,-1),f(4,3),q(4,-1)$
d $n(0,-5),f(4,-1),q(4,-5)$

Explanation:

Step1: Determine the original coordinates

From the graph, the original coordinates are \(N(-1, -1)\), \(F(3, 0)\), \(Q(3, -4)\).

Step2: Apply the translation rule \((x,y)\to(x + 1,y-1)\)

For point \(N\):
\(x=-1+1 = 0\), \(y=-1-1=-2\), so \(N'(0,-2)\)
For point \(F\):
\(x = 3+1=4\), \(y=0 - 1=-1\), so \(F'(4,-1)\)
For point \(Q\):
\(x=3 + 1=4\), \(y=-4-1=-5\), so \(Q'(4,-5)\)

Answer:

D. \(N(0, - 5),F(4,-1),Q'(4,-5)\)