Question

1. $y = - 2$

Explanation:

Step1: Find the distance from each point to the line \(y = - 2\)

The formula for reflecting a point \((x,y)\) over the line \(y = k\) is \((x,2k - y)\). Here \(k=-2\).
For point \(K(-1,0)\):
The \(y\) - coordinate of \(K\) is \(y = 0\). Using the formula \(y'=2\times(-2)-0=-4\), and \(x\) - coordinate remains \(x=-1\).
For point \(L(-2,2)\):
The \(y\) - coordinate of \(L\) is \(y = 2\). Using the formula \(y'=2\times(-2)-2=-4 - 2=-6\), and \(x\) - coordinate remains \(x=-2\).
For point \(M(1,4)\):
The \(y\) - coordinate of \(M\) is \(y = 4\). Using the formula \(y'=2\times(-2)-4=-4 - 4=-8\), and \(x\) - coordinate remains \(x = 1\).
For point \(N(2,0)\):
The \(y\) - coordinate of \(N\) is \(y = 0\). Using the formula \(y'=2\times(-2)-0=-4\), and \(x\) - coordinate remains \(x = 2\).

Answer:

\(K'(-1,-4)\), \(L'(-2,-6)\), \(M'(1,-8)\), \(N'(2,-4)\)