Question

graph the image of square efgh after the following glide reflection:
translation 18 units right
reflection across the line y = 1

Explanation:

Step1: Find coordinates of original square

Assume coordinates: \(E(-11,13)\), \(F(-3,11)\), \(G(-5,5)\), \(H(-11,7)\)

Step2: Apply translation (add 18 to x - coordinate)

\(E'(-11 + 18,13)=(7,13)\), \(F'(-3+18,11)=(15,11)\), \(G'(-5 + 18,5)=(13,5)\), \(H'(-11+18,7)=(7,7)\)

Step3: Apply reflection across \(y = 1\) (use formula \(y=2\times1 - y_{old}\))

For \(E'(7,13)\): \(y = 2\times1-13=-11\), so \(E''(7,-11)\)
For \(F'(15,11)\): \(y = 2\times1 - 11=-9\), so \(F''(15,-9)\)
For \(G'(13,5)\): \(y=2\times1 - 5=-3\), so \(G''(13,-3)\)
For \(H'(7,7)\): \(y=2\times1 - 7=-5\), so \(H''(7,-5)\)

Step4: Plot new points \(E''(7,-11)\), \(F''(15,-9)\), \(G''(13,-3)\), \(H''(7,-5)\) and connect them

Answer:

Plot the points \((7,-11)\), \((15,-9)\), \((13,-3)\), \((7,-5)\) on the coordinate - plane and connect them to form the image of the square after glide - reflection.