Question

1. quadrilateral krwb is shown on the coordinate grid.

a. apply the sequence of transformations to quadrilateral krwb. draw the result of each transformation on the coordinate grid.

• (x,y)→(x, -y) label as krwb.
• (x,y)→(x + 10,y + 6) label as krwb.

Explanation:

Step1: Identify original coordinates

Let's assume the coordinates of the vertices of quadrilateral \(KRWB\) are \(K(x_1,y_1)\), \(R(x_2,y_2)\), \(W(x_3,y_3)\), \(B(x_4,y_4)\). From the graph, if we estimate: \(K(-8,4)\), \(R(-2,6)\), \(W(3,1)\), \(B(-6,2)\)

Step2: Apply first transformation \((x,y)\to(x, - y)\)

For point \(K(-8,4)\), the new - point \(K'(-8,-4)\); for \(R(-2,6)\), \(R'(-2,-6)\); for \(W(3,1)\), \(W'(3,-1)\); for \(B(-6,2)\), \(B'(-6,-2)\)

Step3: Apply second transformation \((x,y)\to(x + 10,y + 6)\)

For point \(K'(-8,-4)\), \(K''=(-8 + 10,-4+6)=(2,2)\); for \(R'(-2,-6)\), \(R''=(-2 + 10,-6 + 6)=(8,0)\); for \(W'(3,-1)\), \(W''=(3 + 10,-1+6)=(13,5)\); for \(B'(-6,-2)\), \(B''=(-6 + 10,-2+6)=(4,4)\)

Step4: Draw on coordinate grid

Plot the points \(K(-8,4)\), \(R(-2,6)\), \(W(3,1)\), \(B(-6,2)\) for the original quadrilateral. Then plot \(K'(-8,-4)\), \(R'(-2,-6)\), \(W'(3,-1)\), \(B'(-6,-2)\) for the first - transformed quadrilateral. Finally, plot \(K''(2,2)\), \(R''(8,0)\), \(W''(13,5)\), \(B''(4,4)\) for the second - transformed quadrilateral on the coordinate grid.

Answer:

The new coordinates of the vertices of the quadrilateral after the two - step transformation are \(K''(2,2)\), \(R''(8,0)\), \(W''(13,5)\), \(B''(4,4)\) and they should be plotted on the coordinate grid as described above.