Question

find the coordinates of the point 3/10 of the way from a to b. the coordinates of the point 3/10 of the way from a to b are (type an ordered - pair).

Explanation:

Step1: Identify coordinates of A and B

Let \(A=(x_1,y_1)=(- 8,4)\) and \(B=(x_2,y_2)=(10,-5)\).

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, the point is \(\frac{3}{10}\) of the way from \(A\) to \(B\), so \(m = 3\) and \(n=7\).
For the \(x\) - coordinate:
\[

$$\begin{align*} x&=\frac{3\times10 + 7\times(-8)}{3 + 7}\\ &=\frac{30-56}{10}\\ &=\frac{-26}{10}\\ &=-2.6 \end{align*}$$

\]
For the \(y\) - coordinate:
\[

$$\begin{align*} y&=\frac{3\times(-5)+7\times4}{3 + 7}\\ &=\frac{-15 + 28}{10}\\ &=\frac{13}{10}\\ &=1.3 \end{align*}$$

\]

Answer:

\((-2.6,1.3)\)