Question

1. write a rule describing the translation below:

rule: _

1. write a rule describing the translation below:

rule: _

Explanation:

Step1: Find the horizontal and vertical changes for problem 7

Let's take a point \(E\). Suppose \(E\) has coordinates \((x,y)\). \(E'\) has coordinates \((x + 5,y+3)\).
For example, if \(E=( - 1,1)\), then \(E'=(4,4)\). The change in \(x\) - coordinate is \(\Delta x=x_{E'}-x_E=4-(-1) = 5\), and the change in \(y\) - coordinate is \(\Delta y=y_{E'}-y_E=4 - 1=3\).
The translation rule for a point \((x,y)\) is \((x,y)\to(x + 5,y + 3)\)

Step2: Find the horizontal and vertical changes for problem 8

Let's take a point \(M\). Suppose \(M\) has coordinates \((x,y)\). \(M'\) has coordinates \((x-2,y + 1)\).
For example, if \(M=(3,2)\), then \(M'=(1,3)\). The change in \(x\) - coordinate is \(\Delta x=x_{M'}-x_M=1 - 3=-2\), and the change in \(y\) - coordinate is \(\Delta y=y_{M'}-y_M=3 - 2 = 1\).
The translation rule for a point \((x,y)\) is \((x,y)\to(x-2,y + 1)\)

Answer:

1. \((x,y)\to(x + 5,y + 3)\)
2. \((x,y)\to(x-2,y + 1)\)