Question

4.1 engage: grid transformations
due on 10.30.2025 10 total points 2 total attempts
answer the question correctly to continue:
a point moves from
(3,4) to (6,7). what was
the translation rule?

Explanation:

Step1: Calculate the change in x - coordinate

The initial x - coordinate is \(x_1 = 3\), and the final x - coordinate is \(x_2=6\). The change in the x - coordinate \(\Delta x=x_2 - x_1\).
\(\Delta x=6 - 3=3\)

Step2: Calculate the change in y - coordinate

The initial y - coordinate is \(y_1 = 4\), and the final y - coordinate is \(y_2 = 7\). The change in the y - coordinate \(\Delta y=y_2 - y_1\).
\(\Delta y=7 - 4=3\)

Step3: Determine the translation rule

The translation rule for a point \((x,y)\) is \((x,y)\to(x+\Delta x,y + \Delta y)\). Substituting \(\Delta x = 3\) and \(\Delta y=3\), we get \((x,y)\to(x + 3,y+3)\)

Answer:

\((x,y)\to(x + 3,y+3)\) (the third option in the given choices)