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 \((x,y)\) \(k\) units down, the transformation rule is \((x,y - k)\). Here \(x = 5\), \(y=7\) and \(k = 4\). So 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 transformation rule is \((-x,y)\). For the point \((5,3)\), after reflection over the \(y\) - axis, the \(x\) - coordinate changes its sign. So the new point is \((- 5,3)\).

Answer:

\(-5\)