Question

write the coordinates of the vertices after a translation 4 units right and 1 unit up.

Explanation:

1. First, identify the original coordinates of the vertices:

• Assume the coordinates of point \(C\) are \((x_1,y_1)\), point \(D\) are \((x_2,y_2)\), and point \(E\) are \((x_3,y_3)\). From the graph, \(C(-6, - 9)\), \(D(-6,-3)\), \(E(-2,-7)\).

1. Then, apply the translation rule:

• The translation rule for moving 4 units right and 1 unit up is \((x,y)\to(x + 4,y + 1)\).
• For point \(C(-6,-9)\):
• Calculate the new - \(x\) - coordinate: \(x=-6 + 4=-2\).
• Calculate the new - \(y\) - coordinate: \(y=-9 + 1=-8\). So the new coordinates of \(C\) are \((-2,-8)\).
• For point \(D(-6,-3)\):
• Calculate the new - \(x\) - coordinate: \(x=-6 + 4=-2\).
• Calculate the new - \(y\) - coordinate: \(y=-3 + 1=-2\). So the new coordinates of \(D\) are \((-2,-2)\).
• For point \(E(-2,-7)\):
• Calculate the new - \(x\) - coordinate: \(x=-2 + 4 = 2\).
• Calculate the new - \(y\) - coordinate: \(y=-7 + 1=-6\). So the new coordinates of \(E\) are \((2,-6)\).

Answer:

The new coordinates of \(C\) are \((-2,-8)\), the new coordinates of \(D\) are \((-2,-2)\), and the new coordinates of \(E\) are \((2,-6)\).