(a)
To plot: The point
(a)
Explanation of Solution
Given information: The reflection in the line
Graph:
If the reflection line is
If the reflection line is y -axis, then the mapping is:
The composition of
So, the image of point
Plot the point
Figure (1)
Interpretation: From the figure it can be observed that to draw the image of point Q , plot the image of point
(b)
To find: The value of
(b)
Answer to Problem 25WE
The value of
Explanation of Solution
Given information: The reflection in the line
Calculation:
As per the theorem 14-8, composite of reflections in two intersecting lines is a rotation about the point of intersection of the two lines. The
The angle of rotation or
Therefore, the value of
(c)
To verify: The line
(c)
Explanation of Solution
Given information: The reflection in the line
Proof:
From part (a), the image of point
The slope of line OP that passes through the points
The slope of line OQ that passes through the points
Now,
As the product of lines OP and OQ is
Hence, it is proved that
(d)
To find: The image of
(d)
Answer to Problem 25WE
The image of
Explanation of Solution
Given information: The reflection in the line
Calculation:
The image of point
The image of point
Now, the image of point
Now, the image of point
Therefore, the image of
Chapter 14 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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