Question

find the coordinates of the vertices of each figure after the translation: (x, y)→(x - 5, y + 1)

Explanation:

Step1: Identify original coordinates

Assume the original coordinates of vertices of the polygon are \(B(x_1,y_1)\), \(C(x_2,y_2)\), \(D(x_3,y_3)\), \(E(x_4,y_4)\). From the grid - if we assume \(B(-2,2)\), \(C(1,1)\), \(D(0, - 2)\), \(E(-3,-2)\).

Step2: Apply the translation rule \((x,y)\to(x - 5,y + 1)\)

For point \(B\):
New \(x\) - coordinate: \(x_1-5=-2 - 5=-7\)
New \(y\) - coordinate: \(y_1 + 1=2 + 1=3\)
For point \(C\):
New \(x\) - coordinate: \(x_2-5=1 - 5=-4\)
New \(y\) - coordinate: \(y_2 + 1=1+1 = 2\)
For point \(D\):
New \(x\) - coordinate: \(x_3-5=0 - 5=-5\)
New \(y\) - coordinate: \(y_3 + 1=-2 + 1=-1\)
For point \(E\):
New \(x\) - coordinate: \(x_4-5=-3 - 5=-8\)
New \(y\) - coordinate: \(y_4 + 1=-2 + 1=-1\)

Answer:

The new coordinates of \(B\) are \((-7,3)\), of \(C\) are \((-4,2)\), of \(D\) are \((-5,-1)\), of \(E\) are \((-8,-1)\)