Question

draw the image of quadrilateral abcd under the translation (x,y)→(x + 4,y - 3).

Explanation:

Step1: Identify coordinates of ABCD

Assume \(A(x_A,y_A)\), \(B(x_B,y_B)\), \(C(x_C,y_C)\), \(D(x_D,y_D)\) from the graph. Let's say \(A(2,0)\), \(B(- 1,-2)\), \(C(-7,1)\), \(D(-3,1)\)

Step2: Apply translation rule to point A

For point \(A(2,0)\), using the rule \((x,y)\to(x + 4,y-3)\), we have \(x'_A=2 + 4=6\) and \(y'_A=0-3=-3\). So \(A'(6,-3)\)

Step3: Apply translation rule to point B

For point \(B(-1,-2)\), \(x'_B=-1 + 4=3\) and \(y'_B=-2-3=-5\). So \(B'(3,-5)\)

Step4: Apply translation rule to point C

For point \(C(-7,1)\), \(x'_C=-7 + 4=-3\) and \(y'_C=1-3=-2\). So \(C'(-3,-2)\)

Step5: Apply translation rule to point D

For point \(D(-3,1)\), \(x'_D=-3 + 4=1\) and \(y'_D=1-3=-2\). So \(D'(1,-2)\)

Step6: Plot new points

Plot points \(A'(6,-3)\), \(B'(3,-5)\), \(C'(-3,-2)\), \(D'(1,-2)\) on the same coordinate - plane and connect them in order to get the translated quadrilateral.

Answer:

Plot points \(A'(6,-3)\), \(B'(3,-5)\), \(C'(-3,-2)\), \(D'(1,-2)\) and connect them to form the translated quadrilateral.