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? o t_{-4,3}(x,y) o t_{-4,1}(x,y) o t_{4,-1}(x,y) o t_{4,-3}(x,y)

Explanation:

Step1: Find change in x - coordinate

To find the change in the x - coordinate, subtract the x - coordinate of the original point from the x - coordinate of the translated point. For point A, \(x_{A'}=-10\) and \(x_A = - 6\). The change in x, \(\Delta x=-10-(-6)=-4\).

Step2: Find change in y - coordinate

To find the change in the y - coordinate, subtract the y - coordinate of the original point from the y - coordinate of the translated point. For point A, \(y_{A'}=1\) and \(y_A=-2\). The change in y, \(\Delta y = 1-(-2)=3\).

Step3: Determine the translation rule

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

Answer:

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