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The point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1 : 1 lies in the
- a)first quadrant
- b)second quadrant
- c)third quadrant
- d)fourth quadrant
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The point that divides the line joining the points (1, 2) and (3, 4) i...
Explanation:
To find the point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1:1, we can use the section formula.
Section Formula:
The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Let's assume the coordinates of the point we are looking for are (x, y). We need to find the values of x and y.
Formula:
The section formula states that if a line segment is divided by a point (x, y) internally in the ratio m:n, then the coordinates of the point are given by:
x = (mx₁ + nx₂) / (m + n)
y = (my₁ + ny₂) / (m + n)
Here, (x₁, y₁) = (1, 2) and (x₂, y₂) = (3, 4).
The ratio m:n = 1:1.
Calculations:
Using the section formula, we can calculate the values of x and y.
x = (1*1 + 1*3) / (1 + 1) = (1 + 3) / 2 = 4 / 2 = 2
y = (1*2 + 1*4) / (1 + 1) = (2 + 4) / 2 = 6 / 2 = 3
Therefore, the point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1:1 is (2, 3).
Quadrant:
The point (2, 3) lies in the first quadrant because both the x-coordinate and y-coordinate are positive.
Hence, the correct answer is option 'A' - first quadrant.
To find the point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1:1, we can use the section formula.
Section Formula:
The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Let's assume the coordinates of the point we are looking for are (x, y). We need to find the values of x and y.
Formula:
The section formula states that if a line segment is divided by a point (x, y) internally in the ratio m:n, then the coordinates of the point are given by:
x = (mx₁ + nx₂) / (m + n)
y = (my₁ + ny₂) / (m + n)
Here, (x₁, y₁) = (1, 2) and (x₂, y₂) = (3, 4).
The ratio m:n = 1:1.
Calculations:
Using the section formula, we can calculate the values of x and y.
x = (1*1 + 1*3) / (1 + 1) = (1 + 3) / 2 = 4 / 2 = 2
y = (1*2 + 1*4) / (1 + 1) = (2 + 4) / 2 = 6 / 2 = 3
Therefore, the point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1:1 is (2, 3).
Quadrant:
The point (2, 3) lies in the first quadrant because both the x-coordinate and y-coordinate are positive.
Hence, the correct answer is option 'A' - first quadrant.
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Community Answer
The point that divides the line joining the points (1, 2) and (3, 4) i...
Since the coordinates of both the points are positive, the line joining them lies in the first quadrant. The division of the line in the ratio of 1 : 1 means that the mid-point of this line also lies in the first quadrant, with both coordinates positive.
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The point that divides the line joining the points (1, 2) and (3, 4) internally in the ratio of 1 : 1 lies in thea)first quadrantb)second quadrantc)third quadrantd)fourth quadrantCorrect answer is option 'A'. Can you explain this answer?
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