Question

find the image of (-2, 1) obtained by translating 3 units down, followed by a reflection over the y - axis.
enter the number that belongs in the green box.

Explanation:

Step1: Translate the point 3 units down

For a point \((x,y)\), translating \(k\) units down changes the \(y\) - coordinate. The rule is \((x,y)\to(x,y - k)\). Here \(x=-2,y = 1,k = 3\). So \((-2,1)\to(-2,1 - 3)=(-2,-2)\).

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

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). For the point \((-2,-2)\), when we apply the reflection rule, we get \((-(-2),-2)=(2,-2)\).

Answer:

\(2\)