Question

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

Explanation:

Step1: Translate 4 units down

To translate a point \((x,y)\) \(k\) units down, we subtract \(k\) from the \(y\)-coordinate. So for the point \((5,7)\) translating 4 units down, the new \(y\)-coordinate is \(7 - 4=3\), and the \(x\)-coordinate remains 5. So the point after translation is \((5,3)\).

Step2: Reflect over the y - axis

To reflect a point \((x,y)\) over the \(y\)-axis, we change the sign of the \(x\)-coordinate. For the point \((5,3)\), after reflecting over the \(y\)-axis, the \(x\)-coordinate becomes \(- 5\) and the \(y\)-coordinate remains 3. So the image of the point is \((-5,3)\). The number in the green box (the \(x\)-coordinate) is \(-5\).

Answer:

\(-5\)