Question

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

Explanation:

Step1: Determine the horizontal translation

Let's take a point from the pre - image. Suppose we take the left - most vertex of the pre - image triangle. Let its \(x\) - coordinate be \(x_1\) and the \(x\) - coordinate of the corresponding vertex in the image be \(x_2\).
Count the number of units moved horizontally. If we assume the pre - image point has \(x\) - coordinate \(x = 1\) and the image point has \(x=5\), the horizontal change \(\Delta x=x_2 - x_1=5 - 1 = 4\) (a shift to the right, so positive).

Step2: Determine the vertical translation

Count the number of units moved vertically. Let the \(y\) - coordinate of the pre - image point be \(y_1\) and the \(y\) - coordinate of the image point be \(y_2\). If \(y_1 = 1\) and \(y_2=4\), the vertical change \(\Delta y=y_2 - y_1=4 - 1=3\) (a shift up, so positive).

The translation rule \((x,y)\to(x + 4,y + 3)\)

Answer:

\((x + 4,y + 3)\)