Question

which rule represents the translation from the pre - image, △abc, to the image, △abc? (x, y)→(x + 7, y - 6) (x, y)→(x + 7, y + 6) (x, y)→(x - 6, y + 7) (x, y)→(x + 6, y + 7)

Explanation:

Step1: Analyze horizontal movement

Count the number of units the triangle moves horizontally. Point A moves from \(x = - 3\) to \(x=4\), which is a movement of \(4-(-3)=7\) units to the right. In a translation rule \((x,y)\to(x + a,y + b)\), a right - ward movement is represented by \(a>0\). So, the \(x\) - coordinate changes by \(+7\).

Step2: Analyze vertical movement

Count the number of units the triangle moves vertically. Point A moves from \(y = 4\) to \(y=-2\), which is a movement of \(4-(-2) = 6\) units down. In a translation rule \((x,y)\to(x + a,y + b)\), a downward movement is represented by \(b<0\). So, the \(y\) - coordinate changes by \(-6\).

Answer:

\((x,y)\to(x + 7,y - 6)\)