Question

point $p(1,5)$ is the image of $p(-3,1)$ under a translation.
determine the translation.
use non - negative numbers.
a translation by \boxed{} units to the right/left and \boxed{} units up/down

Explanation:

Step1: Find horizontal translation

To find the horizontal translation, we calculate the difference between the x - coordinates of \(P'\) and \(P\). The formula for the horizontal change (\(\Delta x\)) is \(x_{P'}-x_{P}\). Given \(x_{P}=- 3\) and \(x_{P'}=1\), then \(\Delta x=1 - (-3)=1 + 3 = 4\). Since the result is positive, the translation is to the right.

Step2: Find vertical translation

To find the vertical translation, we calculate the difference between the y - coordinates of \(P'\) and \(P\). The formula for the vertical change (\(\Delta y\)) is \(y_{P'}-y_{P}\). Given \(y_{P}=1\) and \(y_{P'}=5\), then \(\Delta y = 5-1=4\). Since the result is positive, the translation is up.

Answer:

A translation by \(4\) units to the right and \(4\) units up.