Question

1. segment wx: w(-4,6), x <-4,1>; reflection: x - axis; rotation: 90° about origin

1. segment ab: a(-3,2), b(3,8); rotation: 90° clockwise; translation: <-2,-1>

Explanation:

Step1: Solve for Segment WX: Reflect over x-axis

Reflection rule over x-axis: $(x,y)\to(x,-y)$
For $W(-4,6)$: $W'(-4, -6)$
For $X(-4,1)$: $X'(-4, -1)$

Step2: Rotate 90° about origin

Rotation 90° about origin rule: $(x,y)\to(-y,x)$
For $W'(-4, -6)$: $W''(6, -4)$
For $X'(-4, -1)$: $X''(1, -4)$

Step3: Solve for Segment AB: Rotate 90° clockwise

Rotation 90° clockwise rule: $(x,y)\to(y,-x)$
For $A(-3,2)$: $A'(2, 3)$
For $B(3,8)$: $B'(8, -3)$

Step4: Apply translation $<-2,-1>$

Translation rule: $(x,y)\to(x-2,y-1)$
For $A'(2, 3)$: $A''(0, 2)$
For $B'(8, -3)$: $B''(6, -4)$

Answer:

1. Final coordinates for segment WX: $W''(6, -4)$, $X''(1, -4)$
2. Final coordinates for segment AB: $A''(0, 2)$, $B''(6, -4)$

To plot these:

• For WX: Plot (6, -4) and (1, -4), connect the points.
• For AB: Plot (0, 2) and (6, -4), connect the points.