Answer:
The coordinates of the point that is 1/5 the way from A to B is [tex](x,y) = (-5,\frac{26}{5})[/tex]
Step-by-step explanation:
Here, the given points are: A (-7,4) and B (3,10)
Let us assume the point M(x,y) on AB is such that
AM : AB = 1 : 5
⇒ AM : (AB - AM) = 1 : (5-1) = 1: 4
⇒ AM : MB = 1 : 4
Now, The Section Formula states the coordinates of point (x,y) on any line dividing the line in the ratio m1 : m2
[tex](x,y) = (\frac{m_2x_1+m_1x_2}{m_1+m_2} ,\frac{m_2y_1+m_1y_2}{m_1+m_2} )[/tex]
Here, in the given equation, m1: m2 = 1:4
So, the coordinates M(x,y) is given as:
[tex](x,y) = (\frac{(-7)(4) + 1 (3)}{1+ 4} ,\frac{4(4) + 1(10)}{1+4} )\\\implies (x,y) = (\frac{-28+3}{5} ,\frac{16+10}{5} ) = (\frac{-25}{5} ,\frac{26}{5} )\\\implies (x,y) = (-5,\frac{26}{5} )[/tex]
Hence, the coordinates of the point that is 1/5 the way
from A to B is [tex](x,y) = (-5,\frac{26}{5})[/tex]
