Question

1. apply a reflection over the y - axis followed by a translation right 3 units to point (5,4). what is the original point? (2,4) (-2,4) (-5,4) (2,-4)

Explanation:

Step1: Find the point before translation

Let the point after reflection be \((x,y)\). The rule for translation right \(3\) units is \((x,y)\to(x + 3,y)\). If the final point is \((5,4)\), then \(x+3 = 5\) and \(y = 4\). Solving \(x+3 = 5\) gives \(x=5 - 3=2\). So the point before translation is \((2,4)\).

Step2: Find the original point

The rule for reflection over the \(y -\)axis is \((x,y)\to(-x,y)\). Let the original point be \((a,b)\). If the point after reflection is \((2,4)\), then \(-a=2\) and \(b = 4\). Solving \(-a = 2\) gives \(a=-2\).

Answer:

\((-2,4)\)