Question

The point P divides the line segment AB joining points A (2, 1) and B (-3, 6) in the ratio
2:3. Does point P lie on the line x-5y+15=0? Justify.

Answer 1

Answer:

Hola‼.........✌

The Point P lies on the given equation.

We are given the following in the question:

Point p divides the line segment joining the points (2,1) and (-3,6) in the ratio 2:3

By section formula :

If (x,y) divides the line segment in the ratio m:n

{(mx2 + nx1) /m+n, ( my2 + ny1)/ m+n}

coordinates of p can be calculated as:

P(x,y) = {2×(-3) +3×2}/ 2+3, { (2×6 +3×1)/ 2+3}

P(x,y) = (0,3)

Given the equation,

x-5y +15= 0

Putting x= 0, y=3

=> 0- 5×3 + 15= 0

Since, the coordinated of p satisfies the given equation, the point p lies on the given equation.

(justified)

Hope it’s helpful.... ☺