Question

graph the image of kite efgh after a reflection over the line y = 4.

Explanation:

Step1: Find the distance from each point to the line \(y = 4\)

For a point \((x,y)\), the distance to the line \(y = 4\) is \(d=|y - 4|\).
For point \(E(-2,-1)\), \(d_E=| - 1-4|=5\).
For point \(F(1,0)\), \(d_F=|0 - 4| = 4\).
For point \(G(-2,2)\), \(d_G=|2 - 4|=2\).
For point \(H(-5,0)\), \(d_H=|0 - 4| = 4\).

Step2: Reflect each point over the line \(y = 4\)

The formula for reflecting a point \((x,y)\) over the line \(y = 4\) is \((x,4+(4 - y))=(x,8 - y)\).
For point \(E(-2,-1)\), the reflected point \(E'(-2,8-(-1))=(-2,9)\).
For point \(F(1,0)\), the reflected point \(F'(1,8 - 0)=(1,8)\).
For point \(G(-2,2)\), the reflected point \(G'(-2,8 - 2)=(-2,6)\).
For point \(H(-5,0)\), the reflected point \(H'(-5,8 - 0)=(-5,8)\).

Step3: Plot the reflected points and connect them

Plot the points \(E'(-2,9)\), \(F'(1,8)\), \(G'(-2,6)\), \(H'(-5,8)\) on the coordinate - plane and connect them in the same order as the original kite \(EFGH\) (i.e., \(E'\to F'\to G'\to H'\to E'\)) to form the reflected kite.

Answer:

Plot the points \(E'(-2,9)\), \(F'(1,8)\), \(G'(-2,6)\), \(H'(-5,8)\) and connect them to get the reflected kite.