Question

find the coordinates of the point $\frac{3}{10}$ of the way from a to b.
the coordinates of the point $\frac{3}{10}$ of the way from a to b are
(type an ordered - pair.)

Explanation:

Step1: Identify coordinates of A and B

Let \(A=(x_1,y_1)=(- 4,-8)\) and \(B=(x_2,y_2)=(6,6)\)

Step2: Use the section - formula

The formula for the coordinates of a point \(P=(x,y)\) that divides the line - segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 3\) and \(n=10 - 3=7\).
For the x - coordinate:
\[x=\frac{3\times6+7\times(-4)}{3 + 7}=\frac{18-28}{10}=\frac{-10}{10}=-1\]
For the y - coordinate:
\[y=\frac{3\times6+7\times(-8)}{3 + 7}=\frac{18-56}{10}=\frac{-38}{10}=-3.8\]

Answer:

\((-1,-3.8)\)