Question

Locate the point on the line segment between A(3,-5) and B(13,-15) given that the point is 4/5 of the way from A to B. Show your work.

Answer 1

[11,-13]

Explanation:

Let P be the point between A(3,-5) and B(13,-15) where segment AP =
`(4)/(5)`th of segment AB.

Therefore, point P divides the line AB in a 4 : 1 ratio internally.

Hence, the coordinates of point P will be
`[(4* 13+ 1 * 3)/(4+1) , (4(-15)+ 1(-5))/(4+1) ]`

= [11,-13] (Answer)

We know that If A
`(x_(1), y_(1) )` and B
`(x_(2), y_(2) )` are two different point and point P(h,k) divides line AB in the ratio m : n internally, then

(h,k) ≡
`((mx_(2)+ n x_(1))/(m+n) , (my_(2)+ny_(1))/(m+n) )`