Question

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

Explanation:

Step1: Identify the coordinates of vertices

Let the coordinates of vertices of quadrilateral \(ABCD\) be \(A(x_A,y_A)\), \(B(x_B,y_B)\), \(C(x_C,y_C)\), \(D(x_D,y_D)\). From the graph, assume \(A(2,0)\), \(B(1, - 2)\), \(C(-7,0)\), \(D(-2,2)\).

Step2: Apply the translation rule

The translation rule is \((x,y)\to(x + 4,y-3)\).
For point \(A\): \(x_A'=x_A + 4=2 + 4=6\), \(y_A'=y_A-3=0 - 3=-3\), so \(A'\) is \((6,-3)\).
For point \(B\): \(x_B'=x_B + 4=1+4 = 5\), \(y_B'=y_B-3=-2-3=-5\), so \(B'\) is \((5,-5)\).
For point \(C\): \(x_C'=x_C + 4=-7 + 4=-3\), \(y_C'=y_C-3=0-3=-3\), so \(C'\) is \((-3,-3)\).
For point \(D\): \(x_D'=x_D + 4=-2 + 4=2\), \(y_D'=y_D-3=2-3=-1\), so \(D'\) is \((2,-1)\).

Step3: Plot the new - vertices

Plot the points \(A'(6,-3)\), \(B'(5,-5)\), \(C'(-3,-3)\), \(D'(2,-1)\) on the same coordinate - grid and connect them in order to get the image of quadrilateral \(ABCD\) under the given translation.

Answer:

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