Question

❤️❤️❤️ HELLO FRIENDS❤️❤️❤️
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HERE IS YOUR QUESTION

A point p divides the line segment

joining the point A(3,-5) andB(-4,8)

such that AP/PB=k/1.if p lies on

the line x+y=0,then find the value

of K.

Answer 1

Given points are A(3, -5) and B(- 4, 8)

P divides AB in the ratio k:1

Using the section formula, we have:

Coordinate of point P are



Now it is given, that P lies on the line x+y=0

Therefore
see in the image


Thus, the value of k is 1/2.

i hope its hlp you

Answer 2

Given points are A(3,-5) and B(-4,8)

Given AP : PB = k : 1.

By section formula, the coordinates of point P are:

⇒ [(mx2 + nx1)/m + n, (my2 + ny1)/m + n]

Here m : n = k : 1 and (x1,y1) = (3,-5) and (x2,y2) = (-4,8).

= > Coordinates of point P are:

$= > [\frac{k(-4) + 1(3)}{k + 1}, \frac{k(8) + 1(-5)}{k + 1}]$

$= > [\frac{-4k + 3}{k + 1}, \frac{8k - 5}{k + 1}]$

Given that point p lies on the line x + y = 0

$= > \frac{-4k + 3}{k + 1} + \frac{8k - 5}{k + 1} = 0$

⇒ -4k + 3 + 8k - 5 = 0

⇒ 4k - 2 = 0

⇒ 4k = 2

⇒ k = 2/4

⇒ k = 1/2.

Therefore, the value of k = 1/2.

Hope this helps!