Question

use the graph below to enter a single translation rule. complete 0 translation rule that describes the translation. (x,y)→□ (type an ordered pair)

Explanation:

Step1: Find the change in x - coordinate

Take a vertex of the pre - image. Let's say the left - most vertex of the pre - image has an x - coordinate. Suppose the x - coordinate of a vertex of the pre - image is \(x_1\) and the x - coordinate of the corresponding vertex of the image is \(x_2\). By observing the graph, if we assume a vertex of the pre - image (e.g., the left - most vertex of the trapezoid) has \(x\) value \(x_1\) and the corresponding vertex of the image has \(x\) value \(x_2\), we find that \(x_2=x_1 + 2\).

Step2: Find the change in y - coordinate

Take the same vertex. Suppose the y - coordinate of a vertex of the pre - image is \(y_1\) and the y - coordinate of the corresponding vertex of the image is \(y_2\). By observing the graph, \(y_2=y_1+6\).

In general, for any point \((x,y)\) in the pre - image, after translation, the new point \((x',y')\) has \(x'=x + 2\) and \(y'=y + 6\). So the translation rule is \((x,y)\to(x + 2,y+6)\)

Answer:

$(x,y)\to(x + 2,y+6)$