Question

What are the coordinates of point b on ac such that ab=2/5ac

Answer 1

Answer:

$(-\frac{36}{7},\frac{40}{7})$

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

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

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

where $(x_1, y_1)$ and $(x_2,y_2)$ are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = $\frac{2\times 2+(-8)\times 5}{2+5}$

  = $-\frac{36}{7}$

y = $\frac{2\times 5+5\times 6}{2+5}$

  = $\frac{40}{7}$

Therefore, coordinates of pint B will be,

$(-\frac{36}{7},\frac{40}{7})$