Question

part c: practice with shapes

1. plot and connect a(2, 3), b(5, 3), c(5, 6), d(2, 6) to form a square

• translate left 4, down 1
• reflect across the y-axis
• rotate 90° clockwise about the origin

Explanation:

Step1: Translate each point left 4, down 1

For a point \((x,y)\), translation left 4 means \(x - 4\), down 1 means \(y - 1\).

• \(A(2,3)\) becomes \(A_1(2 - 4, 3 - 1)=(-2,2)\)
• \(B(5,3)\) becomes \(B_1(5 - 4, 3 - 1)=(1,2)\)
• \(C(5,6)\) becomes \(C_1(5 - 4, 6 - 1)=(1,5)\)
• \(D(2,6)\) becomes \(D_1(2 - 4, 6 - 1)=(-2,5)\)

Step2: Reflect translated points across y - axis

Reflection across \(y\) - axis: \((x,y)\to(-x,y)\).

• \(A_1(-2,2)\) becomes \(A_2(2,2)\)
• \(B_1(1,2)\) becomes \(B_2(-1,2)\)
• \(C_1(1,5)\) becomes \(C_2(-1,5)\)
• \(D_1(-2,5)\) becomes \(D_2(2,5)\)

Step3: Rotate reflected points \(90^\circ\) clockwise about origin

Rotation \(90^\circ\) clockwise about origin: \((x,y)\to(y,-x)\).

• \(A_2(2,2)\) becomes \(A_3(2,-2)\)
• \(B_2(-1,2)\) becomes \(B_3(2,1)\)
• \(C_2(-1,5)\) becomes \(C_3(5,1)\)
• \(D_2(2,5)\) becomes \(D_3(5,-2)\)

Answer:

• After translation: \(A(-2,2)\), \(B(1,2)\), \(C(1,5)\), \(D(-2,5)\)
• After reflection: \(A(2,2)\), \(B(-1,2)\), \(C(-1,5)\), \(D(2,5)\)
• After rotation: \(A(2,-2)\), \(B(2,1)\), \(C(5,1)\), \(D(5,-2)\) (These points can be plotted to show the transformed square)