rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3, -6), and d(-6, -6). the rectangle is translated so…

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) \\)

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) \\)

Answer

Answer:

( 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) ).