Chapter 3.1, Problem 4PSA

a

To determine

To graph : The reflection of triangle PQR over the x axis has to be plotted with coordinates

Explanation of Solution

Given information : The following information is given regarding the coordinates of the original triangle

  $P=(-5,0)$

  $Q=(-2,6)$

  $R=(7,0)$

Thus, the triangle is as follows

  

Graph : Hence, we sketch the reflection of triangle PQR over the x axis. We thus get

  

Thus, the coordinates for the new diagram are

  $P=(-5,0)$

  $Q=(-2,-6)$

  $R=(7,0)$

Interpretation : Thus, we can see from the above diagram that for reflection over the x axis,

  $y\to -y$

b

To determine

To graph : The reflection of triangle PQR over the y axis has to be plotted with coordinates

Explanation of Solution

Given information : The following information is given regarding the coordinates of the original triangle

  $P=(-5,0)$

  $Q=(-2,6)$

  $R=(7,0)$

Thus, the triangle is as follows

  

Graph : Hence, we sketch the reflection of triangle PQR over the x axis. We thus get

  

Thus, the coordinates for the new diagram are

  $P=(5,0)$

  $Q=(2,-6)$

  $R=(-7,0)$

Interpretation : Thus, we can see from the above diagram that for reflection over the x axis,

  $x\to -x$

c

To determine

To graph : The slide of triangle PQR 3 units in the direction of PR has to be plotted with coordinates

Explanation of Solution

Given information : The following information is given regarding the coordinates of the original triangle

  $P=(-5,0)$

  $Q=(-2,6)$

  $R=(7,0)$

Thus, the triangle is as follows

  

Graph : Hence, we sketch the slide of triangle PQR 3 units in the direction of PR. We thus get

  

Thus, the coordinates for the new diagram are

  $P=(-8,0)$

  $Q=(-5,-6)$

  $R=(4,0)$

Interpretation : Thus, we can see from the above diagram that for reflection over the x axis,

  $x\to x-3$