Question

rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3. -6), and d(-6, -6). the rectangle is translated so that the coordinates of the image are a(-10, 1), b(-7,1), c(-7, -3), and d(-10, -3). which rule was used to translate the image? t_{-4,3}(x,y) t_{-4,1}(x,y) t_{4,-1}(x,y) t_{4,-3}(x,y)

Explanation:

Step1: Calculate the change in x - coordinate

For point \(A(-6,-2)\) and \(A'(-10,1)\), the change in \(x\) is \(\Delta x=-10 - (-6)=- 4\).
For point \(B(-3,-2)\) and \(B'(-7,1)\), the change in \(x\) is \(\Delta x=-7-(-3)=-4\).

Step2: Calculate the change in y - coordinate

For point \(A(-6,-2)\) and \(A'(-10,1)\), the change in \(y\) is \(\Delta y = 1-(-2)=3\).
For point \(B(-3,-2)\) and \(B'(-7,1)\), the change in \(y\) is \(\Delta y=1 - (-2)=3\).

The translation rule \(T_{a,b}(x,y)=(x + a,y + b)\), where \(a=-4\) and \(b = 3\)

Answer:

\(T_{-4,3}(x,y)\)