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: Find the change in x-coordinate

Take point \( A(-6, -2) \) and its image \( A'(-10, 1) \). The change in x - coordinate (\( \Delta x \)) is \( x_{A'} - x_{A}=-10 - (-6)=-10 + 6=-4 \).

Step2: Find the change in y-coordinate

The change in y - coordinate (\( \Delta y \)) is \( y_{A'} - y_{A}=1-(-2)=1 + 2 = 3 \).

Step3: Determine the translation rule

A translation rule \( T_{a,b}(x,y) \) means that we add \( a \) to the x - coordinate and \( b \) to the y - coordinate of the original point, i.e., \( (x + a,y + b) \). Since \( a=-4 \) and \( b = 3 \), the translation rule is \( T_{-4,3}(x,y) \).

Answer:

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