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 4 units down

When translating a point \((x,y)\) down by \(k\) units, the new \(y -\)coordinate is \(y - k\). Here \(x = 5,y = 7,k=4\).
The new point after translation is \((5,7 - 4)=(5,3)\).

Step2: Reflect the translated point 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 \((- 5,3)\).

Answer:

\(3\)