Question

1. translate the figure 2 units left and 4 units down.

Explanation:

Step1: Identify original coordinates

Assume \(A(0,4)\), \(B(2,3)\), \(C(3,0)\), \(D(0, - 2)\)

Step2: Apply left - translation rule

For a left - translation of 2 units, subtract 2 from the \(x\) - coordinate of each point. New \(x\) - coordinates: \(A:0 - 2=-2\), \(B:2 - 2 = 0\), \(C:3 - 2=1\), \(D:0 - 2=-2\)

Step3: Apply down - translation rule

For a down - translation of 4 units, subtract 4 from the \(y\) - coordinate of each point. New \(y\) - coordinates: \(A:4 - 4 = 0\), \(B:3 - 4=-1\), \(C:0 - 4=-4\), \(D:-2 - 4=-6\)

Step4: Write new coordinates

The new coordinates are \(A'(-2,0)\), \(B'(0,-1)\), \(C'(1,-4)\), \(D'(-2,-6)\)

Answer:

The new coordinates of the vertices of the translated figure are \(A'(-2,0)\), \(B'(0,-1)\), \(C'(1,-4)\), \(D'(-2,-6)\)