Question

WILL MARK BRAINIEST!!! Segment AC has two endpoints; (-2,5) and (2,-5). What are the coordinates of point B on segment AC such that the ratio of AB to BC is 5:1? Any help would be appreciated; first correct answer get brainiest and a 5 star review!

Answer 1

Answer:

$(\frac{4}{3},-\frac{10}{3})$

Step-by-step explanation:

If the extreme ends of a line segment AC are A$(x_1,y_1)$ and C$(x_2,y_2)$.

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = $\frac{mx_2+nx_1}{m+n}$

y = $\frac{my_2+ny_1}{m+n}$

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = $\frac{5\times (2)+1(-2)}{5+1}$

  = $\frac{10-2}{5+1}$

  = $\frac{8}{6}$

  = $\frac{4}{3}$

y = $\frac{5\times (-5)+1(5)}{5+1}$

  = $\frac{-25+5}{6}$

  = $-\frac{20}{6}$

  = $-\frac{10}{3}$

Therefore, coordinates of the point B are $(\frac{4}{3},-\frac{10}{3})$.