Question

1. what will be the translation of a point ( p(-5,2)\to p(-3,-2) )?

( t_{4,-2} )
( t_{2,-4} )
( t_{-4,2} )
( t_{-2,4} )

Explanation:

Step1: Calculate the change in \(x\)-coordinate

The formula for the change in \(x\)-coordinate is \(\Delta x=x_{P'}-x_{P}\).
Given \(x_{P}=-5\) and \(x_{P'}=-3\), then \(\Delta x=-3 - (-5)=-3 + 5 = 2\).

Step2: Calculate the change in \(y\)-coordinate

The formula for the change in \(y\)-coordinate is \(\Delta y=y_{P'}-y_{P}\).
Given \(y_{P}=2\) and \(y_{P'}=-2\), then \(\Delta y=-2 - 2=-4\).

The translation \(T_{\Delta x,\Delta y}\) is \(T_{2,-4}\)

Answer:

\(T_{2,-4}\) (the second option)