Question

consider the translation ((x,y)\to(x + 3,y - 3)). for each of the following, draw the image of the figure under the translation and find the coordinates of the images of the labeled points.

(type an ordered pair )
choose the correct translation below
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

a)
graph of a quadrilateral with vertices labeled a, b, c, d on a coordinate grid
graphs of translated quadrilaterals for options a, b, c, d

Explanation:

Step1: Find coordinates of points

From the graph, \(A(-4,3)\), \(B(-2,3)\), \(C(-2,1)\), \(D(0,1)\)

Step2: Apply translation rule \((x,y)\to(x + 3,y-3)\)

For point \(A\):
\(x=-4,y = 3\)
\(x+3=-4 + 3=-1\), \(y-3=3-3 = 0\)
\(A'(-1,0)\)
For point \(B\):
\(x=-2,y = 3\)
\(x+3=-2+3 = 1\), \(y-3=3 - 3=0\)
\(B'(1,0)\)
For point \(C\):
\(x=-2,y = 1\)
\(x+3=-2 + 3=1\), \(y-3=1-3=-2\)
\(C'(1,-2)\)
For point \(D\):
\(x=0,y = 1\)
\(x+3=0+3 = 3\), \(y-3=1-3=-2\)
\(D'(3,-2)\)

Answer:

\(A'(-1,0)\), \(B'(1,0)\), \(C'(1,-2)\), \(D'(3,-2)\)