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riadik2000 [5.3K]
3 years ago
9

WILL MARK BRAINIEST!!! Segment AC has two endpoints; (-2,5) and (2,-5). What are the coordinates of point B on segment AC such t

hat the ratio of AB to BC is 5:1? Any help would be appreciated; first correct answer get brainiest and a 5 star review!

Mathematics
1 answer:
svet-max [94.6K]3 years ago
6 0

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}).

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