Question

determine the translation. use non - negative numbers. a translation by units to the right and units down

Explanation:

Step1: Observe x - coordinate change

Let the coordinates of point C be \((x_1,y_1)\) and of point \(C'\) be \((x_2,y_2)\). By looking at the grid, assume \(C\) has coordinates \((x_1,y_1)\) and \(C'\) has coordinates \((x_2,y_2)\). Count the horizontal distance between the two points. Moving from \(C\) to \(C'\), we see that the x - coordinate of \(C'\) is less than that of \(C\). The number of units moved horizontally is found by taking the absolute value of the difference in x - coordinates. Since we need non - negative numbers and the movement is to the left (but we are asked to use non - negative numbers for the right - left part in the given format), assume \(C\) is at \(x = 2\) and \(C'\) is at \(x=0\), the number of units to the left is \(|2 - 0|=2\), so the number of units to the right (using non - negative numbers) is \(0\) and to the left is \(2\).

Step2: Observe y - coordinate change

Count the vertical distance between \(C\) and \(C'\). Assume \(C\) is at \(y=-3\) and \(C'\) is at \(y = - 6\). The change in the y - coordinate \(\Delta y=y_2 - y_1=-6-(-3)=- 3\). Since we are asked for non - negative numbers for the up - down part and the movement is downwards, the number of units down is \(|-6-(-3)| = 3\).

Answer:

A translation by \(0\) units to the right and \(3\) units down.