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The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .
- a)lies in the 1st quadrant
- b)lies in 3rd quadrant
- c)lies in the 2nd quadrant
- d)cannot be found
Correct answer is option 'D'. Can you explain this answer?
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The point which divides the joint of (1, 2) and (3,4) externally in th...
as we know that for the co ordinates of a point whic divides externally in ratio m:n
(x,y)=(mx2-nx1)/m-n, (my2-my1)/m-n
let us take x1=1,y1=2
x2=3 , y2=4
m=1, n=1
by the above formula
(1*3-1*1)/1-1 (1*4-1*2)/1-1
we will get x,y as infinity so we can say there is no point which divides line in ratio 1:1 externally for any line joining two points
Most Upvoted Answer
The point which divides the joint of (1, 2) and (3,4) externally in th...
Given Points: (1, 2) and (3, 4)
External Ratio: 1:1
To find the point which divides the line segment joining the given points externally in the ratio 1:1, we can use the section formula. The section formula states that if a line segment joining two points (x1, y1) and (x2, y2) is divided by a point (x, y) in the ratio m:n, then the coordinates of the point (x, y) are given by:
x = (m*x2 + n*x1) / (m + n)
y = (m*y2 + n*y1) / (m + n)
In this case, the given points are (1, 2) and (3, 4), and the external ratio is 1:1. Therefore, m = 1 and n = 1.
Calculating the coordinates of the point using the section formula:
x = (1*3 + 1*1) / (1 + 1) = 4/2 = 2
y = (1*4 + 1*2) / (1 + 1) = 6/2 = 3
So, the coordinates of the point which divides the line segment joining (1, 2) and (3, 4) externally in the ratio 1:1 are (2, 3).
Now, let's analyze the position of this point in the Cartesian coordinate system.
The point (2, 3) lies in the first quadrant if both its x and y coordinates are positive. In this case, both x and y are positive, so the point lies in the first quadrant.
The point (2, 3) lies in the second quadrant if its x coordinate is negative and y coordinate is positive. In this case, the x coordinate is positive, so the point does not lie in the second quadrant.
The point (2, 3) lies in the third quadrant if both its x and y coordinates are negative. In this case, the x coordinate is positive, so the point does not lie in the third quadrant.
Therefore, the correct answer is option 'D' - the position of the point cannot be found, as it does not lie in any specific quadrant.
External Ratio: 1:1
To find the point which divides the line segment joining the given points externally in the ratio 1:1, we can use the section formula. The section formula states that if a line segment joining two points (x1, y1) and (x2, y2) is divided by a point (x, y) in the ratio m:n, then the coordinates of the point (x, y) are given by:
x = (m*x2 + n*x1) / (m + n)
y = (m*y2 + n*y1) / (m + n)
In this case, the given points are (1, 2) and (3, 4), and the external ratio is 1:1. Therefore, m = 1 and n = 1.
Calculating the coordinates of the point using the section formula:
x = (1*3 + 1*1) / (1 + 1) = 4/2 = 2
y = (1*4 + 1*2) / (1 + 1) = 6/2 = 3
So, the coordinates of the point which divides the line segment joining (1, 2) and (3, 4) externally in the ratio 1:1 are (2, 3).
Now, let's analyze the position of this point in the Cartesian coordinate system.
The point (2, 3) lies in the first quadrant if both its x and y coordinates are positive. In this case, both x and y are positive, so the point lies in the first quadrant.
The point (2, 3) lies in the second quadrant if its x coordinate is negative and y coordinate is positive. In this case, the x coordinate is positive, so the point does not lie in the second quadrant.
The point (2, 3) lies in the third quadrant if both its x and y coordinates are negative. In this case, the x coordinate is positive, so the point does not lie in the third quadrant.
Therefore, the correct answer is option 'D' - the position of the point cannot be found, as it does not lie in any specific quadrant.
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The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer?
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The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer?.
The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer?.
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The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The point which divides the joint of (1, 2) and (3,4) externally in the ratio 1 : 1 .a)lies in the1st quadrantb)lies in3rd quadrantc)lies in the2nd quadrantd)cannot be foundCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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