Question

△abc is the image of △abc under a translation. determine the translation. use non - negative numbers. a translation by units to the right/left and units up/down

Explanation:

Step1: Analyze horizontal movement

Let's take a point, say point A. Assume the coordinates of A are \((x_1,y_1)\) and of \(A'\) are \((x_2,y_2)\). By observing the x - coordinates of corresponding points, if \(x_2 x_1\), the movement is to the right. For example, if we assume \(A=(2,-4)\) and \(A'=(- 5,1)\), the change in x - coordinate \(\Delta x=x_2 - x_1=-5 - 2=-7\). So it is 7 units to the left.

Step2: Analyze vertical movement

Looking at the y - coordinates of corresponding points. If \(y_2>y_1\), the movement is up. If \(y_2 < y_1\), the movement is down. Using the same points \(A=(2,-4)\) and \(A'=(-5,1)\), the change in y - coordinate \(\Delta y=y_2 - y_1=1-(-4)=5\). So it is 5 units up.

Answer:

A translation by 7 units to the left and 5 units up.