Question

graph the image of rectangle vwxy after the following glide reflection:
translation 18 units up
reflection across the line $x = 3$

Explanation:

Step1: Find coordinates of original rectangle

Assume coordinates of rectangle \(VWXY\) (from graph): \(V(-2,-6)\), \(W(-8,-6)\), \(X(-8,-14)\), \(Y(-2,-14)\)

Step2: Apply translation 18 units up

Translation rule \((x,y)\to(x,y + 18)\)

• \(V(-2,-6)\to V_1(-2,-6 + 18)=V_1(-2,12)\)
• \(W(-8,-6)\to W_1(-8,-6 + 18)=W_1(-8,12)\)
• \(X(-8,-14)\to X_1(-8,-14 + 18)=X_1(-8,4)\)
• \(Y(-2,-14)\to Y_1(-2,-14 + 18)=Y_1(-2,4)\)

Step3: Apply reflection across \(x = 3\)

Reflection rule \((x,y)\to(6 - x,y)\)

• \(V_1(-2,12)\to V_2(6-(-2),12)=V_2(8,12)\)
• \(W_1(-8,12)\to W_2(6-(-8),12)=W_2(14,12)\)
• \(X_1(-8,4)\to X_2(6-(-8),4)=X_2(14,4)\)
• \(Y_1(-2,4)\to Y_2(6-(-2),4)=Y_2(8,4)\)

Answer:

Plot the points \(V_2(8,12)\), \(W_2(14,12)\), \(X_2(14,4)\), \(Y_2(8,4)\) and connect them to form the image of the rectangle after glide - reflection.