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The condition that the point (x,y) may lie on the line joining (3,4) and (-5,-6) is​
  • a)
    -5x+4y+1=0
  • b)
    -5x-4y+1=0
  • c)
    5x+4y+1=0
  • d)
    5x-4y+1=0
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The condition that the point (x,y) may lie on the line joining (3,4) a...
Since the point P(x,y) lies on the line joining A(3,4) and B(-5,-6), 

Therefore, points P, A and B are collinear points.

So, area of triangle PAB = 0                                         

Therefore, we have: 

10x-18-3y-5y+20=0

10x-8y+2=0

5x-4y+1=0 , which is the required condition. 

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Community Answer
The condition that the point (x,y) may lie on the line joining (3,4) a...
Given points are (3,4) and (-5,-6).

Let (x,y) be a point on the line joining the given points.

Slope of the line joining the given points = (y2-y1)/(x2-x1) = (-6-4)/(-5-3) = -10/-8 = 5/4

Using point-slope form of a line, the equation of the line joining the given points is:

(y-4)/(x-3) = 5/4

Multiplying both sides by 4(x-3), we get:

4(y-4) = 5(x-3)

Expanding, we get:

4y - 16 = 5x - 15

Rearranging, we get:

5x - 4y = 1

Therefore, the correct option is D) 5x - 4y + 1 = 0.
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