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Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)?
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Find the ratio in which the line segment joining points (-3,10) and (6...
Finding the Ratio of Division
To find the ratio in which the line segment joining two points (-3,10) and (6,-8) is divided by a third point (-1,6), we can use the section formula.
Section Formula
The section formula states that if a line segment joining two points A(x1, y1) and B(x2, y2) is divided by a point P(x,y) in the ratio m:n, then the coordinates of point P are given by:
x = (mx2 + nx1)/(m + n)
y = (my2 + ny1)/(m + n)
Calculating the Ratio
Given points A(-3,10), B(6,-8), and P(-1,6), we can substitute the values into the section formula to find the coordinates of point P.
x = (-1*6 + 1*(-3))/(-1 + 1) = (-6 - 3)/0 (division by 0 is undefined)
y = (-8*1 + 6*10)/(1 + 1) = (-8 + 60)/2 = 52/2 = 26
Since the ratio of division is undefined due to division by 0 in the x-coordinate calculation, we can conclude that the point P(-1,6) lies on the line segment joining points A and B. Therefore, the line segment is not divided in any ratio by the point P.
To find the ratio in which the line segment joining two points (-3,10) and (6,-8) is divided by a third point (-1,6), we can use the section formula.
Section Formula
The section formula states that if a line segment joining two points A(x1, y1) and B(x2, y2) is divided by a point P(x,y) in the ratio m:n, then the coordinates of point P are given by:
x = (mx2 + nx1)/(m + n)
y = (my2 + ny1)/(m + n)
Calculating the Ratio
Given points A(-3,10), B(6,-8), and P(-1,6), we can substitute the values into the section formula to find the coordinates of point P.
x = (-1*6 + 1*(-3))/(-1 + 1) = (-6 - 3)/0 (division by 0 is undefined)
y = (-8*1 + 6*10)/(1 + 1) = (-8 + 60)/2 = 52/2 = 26
Since the ratio of division is undefined due to division by 0 in the x-coordinate calculation, we can conclude that the point P(-1,6) lies on the line segment joining points A and B. Therefore, the line segment is not divided in any ratio by the point P.
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Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)?
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Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)?.
Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6)?.
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