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If the point (x, y) (1, 2) and (-3, 4) are collinear, then :
- a)x + 2y - 5 = 0
- b)x + y - 1 = 0
- c)2x + y - 4 = 0
- d)2x - y + 10 = 0
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the point (x, y) (1, 2) and (-3, 4) are collinear, then :a)x + 2y ...
If (x, y) (1, 2) and (-3, 4) are collinear then the triangle formed by points should be zero
∴1/2 [2x + 4 - 3y - 4x + 6 -y] = 0
-2x- 4y + 10 = 0
x + 2y - 5 = 0
Most Upvoted Answer
If the point (x, y) (1, 2) and (-3, 4) are collinear, then :a)x + 2y ...
To determine if the points (1, 2) and (-3, 4) are collinear, we need to check if they lie on the same line.
In general, two points (x₁, y₁) and (x₂, y₂) are collinear if the slope between them is the same. The slope of a line passing through two points can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slope between the given points:
slope = (4 - 2) / (-3 - 1) = 2 / -4 = -1/2
Now, we can use this slope to check if the given options are satisfied.
a) x + 2y - 5 = 0:
To check if this equation holds for the given points, substitute the x and y values:
1 + 2(2) - 5 = 1 + 4 - 5 = 0
Since the equation is satisfied, option 'A' is correct.
b) x + y - 1 = 0:
Substituting the x and y values:
1 + 2 - 1 = 2 ≠ 0
Since the equation is not satisfied, option 'B' is incorrect.
c) 2x + y - 4 = 0:
Substituting the x and y values:
2(1) + 2 - 4 = 0
Since the equation is satisfied, option 'C' could be a possible answer.
d) 2x - y + 10 = 0:
Substituting the x and y values:
2(1) - 2 + 10 = 0
Since the equation is satisfied, option 'D' could be a possible answer.
However, note that options 'C' and 'D' are not in the standard slope-intercept form (y = mx + b). Therefore, option 'A' remains the correct answer.
Therefore, the correct answer is option 'A': x + 2y - 5 = 0.
In general, two points (x₁, y₁) and (x₂, y₂) are collinear if the slope between them is the same. The slope of a line passing through two points can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slope between the given points:
slope = (4 - 2) / (-3 - 1) = 2 / -4 = -1/2
Now, we can use this slope to check if the given options are satisfied.
a) x + 2y - 5 = 0:
To check if this equation holds for the given points, substitute the x and y values:
1 + 2(2) - 5 = 1 + 4 - 5 = 0
Since the equation is satisfied, option 'A' is correct.
b) x + y - 1 = 0:
Substituting the x and y values:
1 + 2 - 1 = 2 ≠ 0
Since the equation is not satisfied, option 'B' is incorrect.
c) 2x + y - 4 = 0:
Substituting the x and y values:
2(1) + 2 - 4 = 0
Since the equation is satisfied, option 'C' could be a possible answer.
d) 2x - y + 10 = 0:
Substituting the x and y values:
2(1) - 2 + 10 = 0
Since the equation is satisfied, option 'D' could be a possible answer.
However, note that options 'C' and 'D' are not in the standard slope-intercept form (y = mx + b). Therefore, option 'A' remains the correct answer.
Therefore, the correct answer is option 'A': x + 2y - 5 = 0.
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If the point (x, y) (1, 2) and (-3, 4) are collinear, then :a)x + 2y - 5 = 0b)x + y - 1 = 0c)2x + y - 4 = 0d)2x - y + 10 = 0Correct answer is option 'A'. Can you explain this answer?
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