Question

find the image of (5,7) obtained by translating 4 units down, followed by a reflection over the y - axis. enter the number that belongs in the green box.

Explanation:

Step1: Translate the point down

When translating a point \((x,y)\) \(4\) units down, we subtract \(4\) from the \(y\) - coordinate.
For the point \((5,7)\), after translation \(4\) units down, the new point is \((5,7 - 4)=(5,3)\).

Step2: Reflect over the \(y\) - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For the point \((5,3)\), after reflection over the \(y\) - axis, the new point is \((- 5,3)\).

The \(x\) - coordinate of the final point (which goes in the green box) is \(-5\).

Answer:

\(-5\)