Question

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

Explanation:

Step1: Assume coordinates of A and B

Let \(A=(x_1,y_1)\) and \(B=(x_2,y_2)\). From the graph, assume \(A = (- 4,6)\) and \(B=(2,-7)\).

Step2: Use the section - formula

The formula for the 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 \(n=7\) (since the point is \(\frac{3}{10}\) of the way from \(A\) to \(B\)).
For the \(x\) - coordinate:
\[x=\frac{3\times2 + 7\times(-4)}{3 + 7}=\frac{6-28}{10}=\frac{-22}{10}=-2.2\]
For the \(y\) - coordinate:
\[y=\frac{3\times(-7)+7\times6}{3 + 7}=\frac{-21 + 42}{10}=\frac{21}{10}=2.1\]

Answer:

\((-2.2,2.1)\)