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Question
The co-ordinate of point A in number line is 5.Find the co-ordinate of points on the same number line which are 13 units away from point A
The co-ordinate of point A in number line is 5.Find the co-ordinate of points on the same number line which are 13 units away from point A
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Solution
This question deals with magnitude, or absolute value if you prefer. A one dimensional vector has two possible directions: positive and negative. A number that is 13 units away from 5 units could be 5+13 or 5–13.
We can show this more rigorously by constructing the equation:
|x−5|=13
To solve this equation, we have to consider the possibility that x-5 is negative and that it is positive:
x−5=13 and x−5=−13
Solving both of these for x yields:
x = −8, x = 18
These are the coordinates you are looking for.
This question deals with magnitude, or absolute value if you prefer. A one dimensional vector has two possible directions: positive and negative. A number that is 13 units away from 5 units could be 5+13 or 5–13.
We can show this more rigorously by constructing the equation:
|x−5|=13
To solve this equation, we have to consider the possibility that x-5 is negative and that it is positive:
x−5=13 and x−5=−13
Solving both of these for x yields:
x = −8, x = 18
These are the coordinates you are looking for.
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