Chapter 11, Problem 7MCQ

To determine

To graph: The given triangle GHJ and its image after a clockwise rotation by 90 degree about vertex H. Also, given the vertices of imaged triangle.

Answer to Problem 7MCQ

Graph of the given figure and its image after given rotation is shown as under:

  

so that the vertices of its imaged triangle be G`(4,2),H`(-3,0) and J`(3,4)

Explanation of Solution

Given information: A triangle GHJ with vertices $G\left(-2,4\right),H\left(-3,0\right)$ and $J(-4,3)$ that to be rotated clockwise by 90 degree around vertex H.

Formula/Concept used: By rule, in rotation by 180 degree around the origin, the original vertex $\left(x,y\right)$ is changed as:

  $\left(x,y\right)\to \left(y,-x\right)$

And the coordinates of the point around which to be rotated, remains the same.

Calculation: Based on above rule, the corresponding vertices of the imaged figure will be:

  $G`(4,2),H`(-3,0)$ and $J`(3,4)$ as the coordinates of point H will remain same.

And on plotting them in XY plane, the graph of image of given figure is shown as:

  

Conclusion: So, imaged triangle G`H`J` is larger than original triangle.