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

Answer:

[11,-13]

Step-by-step explanation:

Let P be the point between A(3,-5) and B(13,-15) where segment AP = $\frac{4}{5}$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 $[\frac{4\times 13+ 1 \times 3}{4+1} , \frac{4(-15)+ 1(-5)}{4+1} ]$

= [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) ≡  $(\frac{mx_{2}+ n x_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n} )$