Chapter 11.3, Problem 2CYU

a)

To determine

To graph: Triangle JKL and its image after a clockwise rotation of 270 degree above vertex J.

Answer to Problem 2CYU

Graph of both the triangles are shown as:

  

Explanation of Solution

Given information: A triangle JKL with vertices $J\left(1,4\right),K\left(1,1\right),L\left(5,1\right)$ that has to be rotated clockwise 270 degree above vertex J.

Formula/Concept used: In clockwise rotation by 270 degree about a fixed point, the coordinates of fixed points remains the same and other coordinate(s)) (x,y) changes using following rule:

  $\left(x,y\right)\to (-y,x)$

Calculation: Based on above rule, the coordinates of imaged vertices are:

  J`(1,4),K`(-1,1),L`(-1,5)

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

  

b)

To determine

To give: The vertices of imaged triangle J`K`L`

Answer to Problem 2CYU

Vertices of imaged triangle J`K`L` are J`(1,4),K`(-1,1),L`(-1,5)

Explanation of Solution

Given information: A triangle JKL with vertices J(1,4),K(1,1),L(5,1)

that has to be rotated clockwise 270 degree above vertex J.

Formula/Concept used: In clockwise rotation by 270 degree about a fixed point, the coordinates of fixed points remains the same and other coordinate(s) (x,y) changes using following rule:

  (x,y)→(-y,x)

Calculation: Based on above rule, on changing the x coordinate from $-y$ and y coordinate to x coordinate, the coordinates of imaged vertices are:

  $J`\left(1,4\right),K`\left(-1,1\right),L`\left(-1,5\right)$

Conclusion: Thus, coordinates of image of triangle JKL be $J`\left(1,4\right),K`\left(-1,1\right),L`\left(-1,5\right)$ .