Question

find the condition for the point (x,y) to lie on the joining (3,4) and (-5,-6)

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Answer 1

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condition that the point (x,y) lies on the line joining (3,4) and (-5,6)
is the line equation joining 3 points  (3,4), (x,y) and (-5,6)
equation (y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁)
substituting....
(y-4)/(x-3) = (6-4)/(-5-3)
x+y-7 = 0

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Answer 2

Given that P(x,y), A(3,4), B(-5,-6).

We know that Line joining equation is:

$= > \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1}$

Here, (x1,y1) = (3,4) and (x2,y2) = (-5,-6).

$= > \frac{y - 4}{x - 3} = \frac{-6 - 4}{-5 - 3}$

$= > \frac{y - 4}{x - 3} = \frac{-10}{-8}$

= > -8(y - 4) = -10(x - 3)

= > -8y + 32 = -10x + 30

= > -10x + 8y - 2 = 0

= > 10x - 8y + 2 = 0

= > 5x - 4y + 1 = 0.

Hope this helps!