Question

graph the image of trapezoid uvwx after the following glide reflection:
translation 15 units down
reflection across the y - axis

Explanation:

Step1: Find coordinates of original trapezoid

Assume coordinates: \(U(-7,3)\), \(V(-2,5)\), \(W(-2,9)\), \(X(-7,11)\)

Step2: Apply translation 15 units down

For a point \((x,y)\), translation 15 units down gives \((x,y - 15)\)
\(U'(-7,3-15)=(-7,-12)\)
\(V'(-2,5 - 15)=(-2,-10)\)
\(W'(-2,9-15)=(-2,-6)\)
\(X'(-7,11 - 15)=(-7,-4)\)

Step3: Apply reflection across the \(y\) - axis

For a point \((x,y)\), reflection across the \(y\) - axis gives \((-x,y)\)
\(U''(7,-12)\)
\(V''(2,-10)\)
\(W''(2,-6)\)
\(X''(7,-4)\)

Answer:

Plot the points \(U''(7,-12)\), \(V''(2,-10)\), \(W''(2,-6)\), \(X''(7,-4)\) and connect them to form the image of the trapezoid after the glide reflection.