Question

a triangle has coordinates f(-2,3), g(-4,1), and h(-2,-2). the triangle is translated and its image has coordinates f(0,0), g(-2,-2), and h(0,-5).
what is the correct rule for the translation?
(x,y)→(x - 2,y-
(x,y)→(x + 2,y-
(x,y)→(x + 2,y-
(x,y)→(x - 3,y-
writing a translation rule
translations
pre-algebra ic sem 2 fall 2025

Explanation:

Step1: Calculate the change in x - coordinate

Take a point, say \(F(-2,3)\) and its image \(F'(0,0)\).
The change in \(x\) - coordinate: \(\Delta x=x_{F'}-x_{F}=0 - (-2)=2\).

Step2: Calculate the change in y - coordinate

The change in \(y\) - coordinate: \(\Delta y=y_{F'}-y_{F}=0 - 3=-3\).
We can check with another point. For point \(G(-4,1)\) and its image \(G'(-2,-2)\).
Change in \(x\) - coordinate: \(\Delta x=-2-(-4) = 2\).
Change in \(y\) - coordinate: \(\Delta y=-2 - 1=-3\).
For point \(H(-2,-2)\) and its image \(H'(0,-5)\).
Change in \(x\) - coordinate: \(\Delta x=0-(-2)=2\).
Change in \(y\) - coordinate: \(\Delta y=-5-(-2)=-3\).

In a translation rule \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal change and \(b\) is the vertical change. Here \(a = 2\) and \(b=-3\).

Answer:

\((x,y)\to(x + 2,y-3)\)