Exam  >   Questions  >  If the three points A(1,6), B(3, –4) an... Start Learning for Free
If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by  x and y is
  • a)
    5x + y – 11= 0
  • b)
    5x + 13y + 5 = 0
  • c)
    5x –13y  + 5 = 0
  • d)
    13x –5y +5 = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the three points A(1,6), B(3, –4) and C(x, y) are collinear t...
Free Test
Community Answer
If the three points A(1,6), B(3, –4) and C(x, y) are collinear t...
Explanation:

Given Points:
- Point A(1,6)
- Point B(3, -4)
- Point C(x, y)

Collinearity of Points:
- Three points are said to be collinear if they lie on the same straight line.

Equation of a Straight Line:
- The general form of the equation of a straight line is Ax + By + C = 0.

Using Slope Formula:
- The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: m = (y2 - y1) / (x2 - x1).
- Slope of line AB: mAB = (-4 - 6) / (3 - 1) = -10 / 2 = -5.
- Slope of line AC: mAC = (y - 6) / (x - 1).
- Since points A, B, and C are collinear, the slopes of AB and AC should be equal.

Equating Slopes:
- Equating slopes: -5 = (y - 6) / (x - 1).
- Simplifying: -5(x - 1) = y - 6.
- Rearranging: -5x + 5 = y - 6.
- Bringing y to the left side: y - 5x - 5 + 6 = 0.
- Final equation: y - 5x + 1 = 0.

Comparison with Options:
- The equation that satisfies the collinearity condition is 5x + y - 1 = 0.
- None of the given options match the equation obtained.
- The closest option is 5x + y - 11 = 0, which is not the same as the derived equation.
Therefore, the correct equation satisfying the collinearity condition for points A, B, and C is y - 5x + 1 = 0, not present in the given options.
Explore Courses for exam
If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer?
Question Description
If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? for 2024 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for . Download more important topics, notes, lectures and mock test series for Exam by signing up for free.
Here you can find the meaning of If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y isa)5x + y – 11= 0b)5x + 13y + 5 = 0c)5x –13y + 5 = 0d)13x –5y +5 = 0Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice tests.
Explore Courses for exam

Top Courses for

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev