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: Analyze the change in \(x\)-coordinate

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

Step2: Analyze the change in \(y\)-coordinate

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

The translation rule \(T_{a,b}(x,y)=(x + a,y + b)\). Here \(a=-4\) (change in \(x\)) and \(b = 3\) (change in \(y\)), so the rule is \(T_{-4,3}(x,y)\)

Answer:

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