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Question 956088: . Which set of points lies on the given graph?
VHS_ALG_S1_07_L203_L303_LQ1-graphic.gif
(Points : 1)
(4, 11), (–2, 7), (1, –1)
(4, 11), (2, –7), (1, 1)
(–4, 11), (–2, 7), (1, –1)
(–4, 11), (–2, 7), (1, 1)
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! check which ones lie in a line:
(4, 11), (–2, 7), (1, –1)
| Solved by pluggable solver: To determine if 3 points lie in a line |
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
 ........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The 3 points do not a same line.
For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
Here the slopes are unequal hence the points do not lie on same line.
To read more on equations of a line refer to articles on wikipedia
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NOT an answer
(4, 11), (2, –7), (1, 1)
| Solved by pluggable solver: To determine if 3 points lie in a line |
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
 ........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The 3 points do not a same line.
For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
Here the slopes are unequal hence the points do not lie on same line.
To read more on equations of a line refer to articles on wikipedia
|
(–4, 11), (–2, 7), (1, –1)
| Solved by pluggable solver: To determine if 3 points lie in a line |
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
 ........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The 3 points do not a same line.
For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
Here the slopes are unequal hence the points do not lie on same line.
To read more on equations of a line refer to articles on wikipedia
|
( ,  ), ( ,  ), ( , )
| Solved by pluggable solver: To determine if 3 points lie in a line |
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The slopes are equal hence the 3 points can lie on same line.
If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line.
 ........................(3)
From (1),(2) and (3)
Hence, It is proved that the 3 points lie on same line.
To read more on equations of a line refer to articles on wikipedia
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your answer is:(, ), (, ), (, )
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