Answer:
![(\frac{4}{3},-\frac{10}{3})](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B3%7D%2C-%5Cfrac%7B10%7D%7B3%7D%29)
Step-by-step explanation:
If the extreme ends of a line segment AC are A
and C
.
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}](https://tex.z-dn.net/?f=%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D)
y = ![\frac{my_2+ny_1}{m+n}](https://tex.z-dn.net/?f=%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Ctimes%20%282%29%2B1%28-2%29%7D%7B5%2B1%7D)
= ![\frac{10-2}{5+1}](https://tex.z-dn.net/?f=%5Cfrac%7B10-2%7D%7B5%2B1%7D)
= ![\frac{8}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B6%7D)
= ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
y = ![\frac{5\times (-5)+1(5)}{5+1}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Ctimes%20%28-5%29%2B1%285%29%7D%7B5%2B1%7D)
= ![\frac{-25+5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B-25%2B5%7D%7B6%7D)
= ![-\frac{20}{6}](https://tex.z-dn.net/?f=-%5Cfrac%7B20%7D%7B6%7D)
= ![-\frac{10}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B10%7D%7B3%7D)
Therefore, coordinates of the point B are
.