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The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :
a. 4 : 2
b. 3 : 4
c. 4 : 5
d. 5 : 6?
a. 4 : 2
b. 3 : 4
c. 4 : 5
d. 5 : 6?
Most Upvoted Answer
The straight line 3x + y = 9 divides the segment joining the points (1...
Solution:
Given:
- Equation of the straight line: 3x + y = 9
- Points: A(1, 3) and B(2, 7)
Formula:
The coordinates of the point dividing the line segment joining two points A(x1, y1) and B(x2, y2) internally in the ratio m1: m2 are given by:
x = (m1x2 + m2x1) / (m1 + m2)
y = (m1y2 + m2y1) / (m1 + m2)
Calculate the point of intersection:
Substitute x = 1 and y = 3 in the equation 3x + y = 9:
3(1) + 3 = 9
3 + 3 = 9
6 ≠ 9
Hence, point A(1, 3) does not lie on the given line.
Substitute x = 2 and y = 7 in the equation 3x + y = 9:
3(2) + 7 = 9
6 + 7 = 9
13 ≠ 9
Hence, point B(2, 7) also does not lie on the given line.
Find the point of intersection of the line and the line joining A and B:
Let the point of intersection be C(x, y).
Using the formula for the point of intersection, we have:
x = (4*2 + 2*1) / (4 + 2) = 10 / 6 = 5/3
y = (4*7 + 2*3) / (4 + 2) = 34 / 6 = 17 / 3
Therefore, the point of intersection is C(5/3, 17/3).
Calculate the ratio:
Now, calculate the ratio in which the line divides the line segment AB:
AC / CB = [(5/3 - 1) / (2 - 5/3)] / [(7 - 17/3) / (17/3 - 3)]
= [(2/3) / (1/3)] / [(14/3) / (2/3)]
= 2 / 7
Therefore, the line divides the line segment AB in the ratio 2:7.
Answer:
The line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio 2:7.
Given:
- Equation of the straight line: 3x + y = 9
- Points: A(1, 3) and B(2, 7)
Formula:
The coordinates of the point dividing the line segment joining two points A(x1, y1) and B(x2, y2) internally in the ratio m1: m2 are given by:
x = (m1x2 + m2x1) / (m1 + m2)
y = (m1y2 + m2y1) / (m1 + m2)
Calculate the point of intersection:
Substitute x = 1 and y = 3 in the equation 3x + y = 9:
3(1) + 3 = 9
3 + 3 = 9
6 ≠ 9
Hence, point A(1, 3) does not lie on the given line.
Substitute x = 2 and y = 7 in the equation 3x + y = 9:
3(2) + 7 = 9
6 + 7 = 9
13 ≠ 9
Hence, point B(2, 7) also does not lie on the given line.
Find the point of intersection of the line and the line joining A and B:
Let the point of intersection be C(x, y).
Using the formula for the point of intersection, we have:
x = (4*2 + 2*1) / (4 + 2) = 10 / 6 = 5/3
y = (4*7 + 2*3) / (4 + 2) = 34 / 6 = 17 / 3
Therefore, the point of intersection is C(5/3, 17/3).
Calculate the ratio:
Now, calculate the ratio in which the line divides the line segment AB:
AC / CB = [(5/3 - 1) / (2 - 5/3)] / [(7 - 17/3) / (17/3 - 3)]
= [(2/3) / (1/3)] / [(14/3) / (2/3)]
= 2 / 7
Therefore, the line divides the line segment AB in the ratio 2:7.
Answer:
The line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio 2:7.
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The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6?
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The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6?.
The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The straight line 3x + y = 9 divides the segment joining the points (1, 3) and (2, 7) in the ratio :a. 4 : 2b. 3 : 4c. 4 : 5d. 5 : 6?.
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