Question

point $c(-4, -3)$ is the image of $c(-2, -3)$ under a translation. determine the translation. use non-negative numbers. a translation by \boxed{} units right/left/up/down

Explanation:

Step1: Analyze x - coordinates

Original x - coordinate: \(x_C=-2\), Image x - coordinate: \(x_{C'}=-4\). The change in x - coordinate is \(\Delta x=x_{C'}-x_C=-4 - (-2)=-2\). A negative change in x - coordinate means a translation to the left. The number of units is \(| - 2| = 2\).

Step2: Analyze y - coordinates

Original y - coordinate: \(y_C=-3\), Image y - coordinate: \(y_{C'}=-3\). The change in y - coordinate is \(\Delta y=y_{C'}-y_C=-3-(-3) = 0\), so there is no vertical translation.

Answer:

A translation by \(2\) units left