Question

triangle xyz is shown on the coordinate plane. if triangle xyz is translated using the rule (x, y)→(x + 1, y - 4) and then reflected across the y - axis to create triangle xyz, what is the location of z? (-2, -1) (-5, 1) (-6, -1) (2, 1)

Explanation:

Answer:

From the coordinate - plane, assume the coordinates of \(Z\) are \((1,3)\).
First, apply the translation \((x,y)\to(x + 1,y - 4)\):
For \(Z(1,3)\), the new coordinates after translation are \((1+1,3 - 4)=(2,-1)\).
Then, apply the reflection across the \(y\) - axis. The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\).
For the point \((2,-1)\), after reflection across the \(y\) - axis, the coordinates of \(Z'\) are \((-2,-1)\).
So the answer is \((-2,-1)\)