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? $\bigcirc t_{-4, 3}(x, y)$ $\bigcirc t_{-4, 1}(x, y)$ $\bigcirc t_{4, -1}(x, y)$ $\bigcirc t_{4, -3}(x, y)$

Explanation:

Step1: Find the change in x-coordinate

For point A: \( -10 - (-6) = -4 \)
For point B: \( -7 - (-3) = -4 \)
So the change in x is -4.

Step2: Find the change in y-coordinate

For point A: \( 1 - (-2) = 3 \)
For point B: \( 1 - (-2) = 3 \)
So the change in y is 3.

Step3: Determine the translation rule

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

Answer:

\( T_{-4, 3}(x,y) \) (corresponding to the first option)