Question

graph the image of quadrilateral fghi after the following glide reflection: translation 17 units down reflection across the line ( x = - 2 )

Explanation:

Step1: Find coordinates of original points

Assume \(F(8,10)\), \(G(3,14)\), \(H(1,8)\), \(I(1,4)\)

Step2: Translate 17 units down

The rule for translation 17 units down is \((x,y)\to(x,y - 17)\)

• \(F(8,10)\to F_1(8,10 - 17)=(8,-7)\)
• \(G(3,14)\to G_1(3,14 - 17)=(3,-3)\)
• \(H(1,8)\to H_1(1,8 - 17)=(1,-9)\)
• \(I(1,4)\to I_1(1,4 - 17)=(1,-13)\)

Step3: Reflect across \(x=-2\)

The rule for reflection across \(x = a\) is \((x,y)\to(2a - x,y)\). Here \(a=-2\), so \((x,y)\to(-4 - x,y)\)

• \(F_1(8,-7)\to F_2(-4 - 8,-7)=(-12,-7)\)
• \(G_1(3,-3)\to G_2(-4 - 3,-3)=(-7,-3)\)
• \(H_1(1,-9)\to H_2(-4 - 1,-9)=(-5,-9)\)
• \(I_1(1,-13)\to I_2(-4 - 1,-13)=(-5,-13)\)

Answer:

Plot the points \(F_2(-12,-7)\), \(G_2(-7,-3)\), \(H_2(-5,-9)\), \(I_2(-5,-13)\) and connect them to form the image of quadrilateral \(FGHI\) after the glide reflection.