Question

graph the image of kite wxyz after the following glide reflection:
translation 15 units right
reflection across the line ( y = 1 )

Explanation:

Step1: Find coordinates of original points

Assume \( Z(-12,6)\), \(W(-8,4)\), \(X(-4,6)\), \(Y(-8,13)\)

Step2: Apply translation 15 units right

Use the rule \((x,y)\to(x + 15,y)\)

• \(Z'(-12+15,6)=(3,6)\)
• \(W'(-8 + 15,4)=(7,4)\)
• \(X'(-4+15,6)=(11,6)\)
• \(Y'(-8 + 15,13)=(7,13)\)

Step3: Apply reflection across \(y = 1\)

Use the rule \((x,y)\to(x,2 - y)\)

• \(Z''(3,2-6)=(3,-4)\)
• \(W''(7,2 - 4)=(7,-2)\)
• \(X''(11,2-6)=(11,-4)\)
• \(Y''(7,2 - 13)=(7,-11)\)

Plot the points \(Z''(3,-4)\), \(W''(7,-2)\), \(X''(11,-4)\), \(Y''(7,-11)\) and connect them to get the image of the kite after glide - reflection.

Answer:

The coordinates of the vertices of the image of kite \(WXYZ\) after glide - reflection are \(Z''(3,-4)\), \(W''(7,-2)\), \(X''(11,-4)\), \(Y''(7,-11)\). Graph these points and connect them to form the required kite.