Question

graph the image of trapezoid uvwx after the following glide reflection:
translation 9 units right
reflection across the line ( y = - 1 )

Explanation:

Step1: Find coordinates of original points

Let's assume the coordinates of \(U(-2,10)\), \(V(-8,8)\), \(W(-8,4)\), \(X(-2,2)\)

Step2: Apply translation 9 units right

The rule for translation 9 units right is \((x,y)\to(x + 9,y)\)

• \(U(-2,10)\to U'(7,10)\)
• \(V(-8,8)\to V'(1,8)\)
• \(W(-8,4)\to W'(1,4)\)
• \(X(-2,2)\to X'(7,2)\)

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

The rule for reflection across \(y = k\) is \((x,y)\to(x,2k - y)\). Here \(k=-1\), so \((x,y)\to(x,-2 - y)\)

• \(U'(7,10)\to U''(7,-12)\)
• \(V'(1,8)\to V''(1,-10)\)
• \(W'(1,4)\to W''(1,-6)\)
• \(X'(7,2)\to X''(7,-4)\)

Answer:

Plot the points \(U''(7,-12)\), \(V''(1,-10)\), \(W''(1,-6)\), \(X''(7,-4)\) and connect them to form the image of the trapezoid after glide - reflection.