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A line is drawn through the points (3 , 4) and (5 , 6) . If the is extended to a point whose ordinate is – 1, then the abscissa of that point is
- a)0
- b)- 2
- c)1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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A line is drawn through the points (3 , 4) and (5 , 6) . If the is ext...
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A line is drawn through the points (3 , 4) and (5 , 6) . If the is ext...
To find the abscissa of the point where the line is extended to an ordinate of 1, let's first find the equation of the line passing through the given points (3, 4) and (5, 6).
Finding the slope of the line:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 4) and (5, 6), the slope of the line is:
m = (6 - 4) / (5 - 3) = 2 / 2 = 1
Finding the equation of the line:
The equation of a line in slope-intercept form is given by:
y = mx + c
Substituting the slope (m = 1) and one of the given points (5, 6) into the equation, we can solve for the y-intercept (c):
6 = 1 * 5 + c
6 = 5 + c
c = 6 - 5
c = 1
So, the equation of the line is:
y = x + 1
Finding the abscissa of the extended point:
The extended point has an ordinate (y-coordinate) of 1. To find the abscissa (x-coordinate), we can substitute this value into the equation of the line and solve for x:
1 = x + 1
x = 1 - 1
x = 0
Therefore, the abscissa of the extended point is 0.
Finding the slope of the line:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 4) and (5, 6), the slope of the line is:
m = (6 - 4) / (5 - 3) = 2 / 2 = 1
Finding the equation of the line:
The equation of a line in slope-intercept form is given by:
y = mx + c
Substituting the slope (m = 1) and one of the given points (5, 6) into the equation, we can solve for the y-intercept (c):
6 = 1 * 5 + c
6 = 5 + c
c = 6 - 5
c = 1
So, the equation of the line is:
y = x + 1
Finding the abscissa of the extended point:
The extended point has an ordinate (y-coordinate) of 1. To find the abscissa (x-coordinate), we can substitute this value into the equation of the line and solve for x:
1 = x + 1
x = 1 - 1
x = 0
Therefore, the abscissa of the extended point is 0.
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A line is drawn through the points (3 , 4) and (5 , 6) . If the is extended to a point whose ordinate is – 1, then the abscissa of that point isa)0b)- 2c)1d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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