Chapter 11.3, Problem 8PPS

a)

To determine

To graph: Trapezoid ABCD and its image after a clockwise rotation of 180 degree about vertex D.

Answer to Problem 8PPS

Vertices of imaged triangle A`B`C`D` are $A`\left(3,-1\right),B`\left(3,-4\right),C`\left(-1,-4\right),D`(-1,1)$ and the graph of both the triangles are shown as:

  

Explanation of Solution

Given information: A triangle JKL with vertices $A\left(-3,1\right),B\left(-3,4\right),C\left(1,4\right),D(-1,1)$ that has to be rotated clockwise 180 degree above vertex D.

Formula/Concept used: In clockwise rotation by 180 degree about a fixed point, the coordinates of fixed points remains the same and other coordinate(s) $\left(x,y\right)$ changes using following rule:

  $\left(x,y\right)\to (-x,-y)$

Calculation: Based on above rule, the coordinates of D will remain same and other vertices will be changed as:

  $A`\left(3,-1\right),B`\left(3,-4\right),C`\left(-1,-4\right),D`(-1,1)$

Conclusion: Thus, the graphs of both the trapezoids are shown as under:

  

b)

To determine

To give: The vertices of imaged trapezoid A`B`C`D`.

Answer to Problem 8PPS

Vertices of imaged triangle A`B`C`D` are: $A`\left(3,-1\right),B`\left(3,-4\right),C`\left(-1,-4\right),D`(-1,1)$ .

Explanation of Solution

Given information: A triangle JKL with vertices $A\left(-3,1\right),B\left(-3,4\right),C\left(1,4\right),D(-1,1)$ that has to be rotated clockwise 180 degree above vertex D.

Formula/Concept used: In clockwise rotation by 180 degree about a fixed point, the coordinates of fixed points remains the same and other coordinate(s) $\left(x,y\right)$ changes using following rule :

  $\left(x,y\right)\to (-x,-y)$

Calculation: Based on above rule, the coordinates of D will remain same and other vertices will be changed as:

   A`(3,-1),B`(3,-4),C`(-1,-4),D`(-1,1)

Conclusion: Thus, Vertices of imaged triangle A`B`C`D` are $A`\left(3,-1\right),B`\left(3,-4\right),C`\left(-1,-4\right),D`(-1,1)$ .