Concept explainers
(a)
Find the symmetry of the points
(a)
Answer to Problem 85E
y − axis symmetry.
Explanation of Solution
Given: Draw two points
Concept Used:
Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. There can also be symmetry in one object, such as a face. If you draw a line of symmetry down the centre of your face, you can see that the left side is a mirror image of the right side. Not all objects have symmetry; if an object is not symmetrical, it is called asymmetric
Calculation:
Let And the both points are reflection of each other with respect to y − axis Therefore they are related as Hence the points are Y − axis symmetry. |
Thus, the points are y − axis symmetry.
(b)
Make a conjecture about any relationship between
(b)
Answer to Problem 85E
Explanation of Solution
Given: Draw two points
Concept Used:
The line (or "axis") of symmetry is the y-axis, also known as the line x = 0. This line is marked green in the picture. The graph is said to be "symmetric about the y-axis", and this line of symmetry is also called the "axis of symmetry"
Calculation:
Draw two points And the both points are reflection of each other with respect to y − axis Therefore they are related as Now we can see the points Since the graph has symmetry to the y − axis, the y − coordinates are the same which means |
Thus,
(c)
Make a conjecture about any relationship between
(c)
Answer to Problem 85E
Explanation of Solution
Given:
Draw two points
Concept Used:
The line (or "axis") of symmetry is the y-axis, also known as the line x = 0. This line is marked green in the picture. The graph is said to be "symmetric about the y-axis", and this line of symmetry is also called the "axis of symmetry"
Calculation:
Draw two points And the both points are reflection of each other with respect to y − axis Therefore they are related as Now we can see the points Since the graph has symmetry to the y − axis, the y − coordinatesare the same but the x − coordinatesare in opposite sign which means |
Thus,
Chapter 4 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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