Question

find the coordinates of the point that partitions $overline{ab}$ in the ratio 3:7.
the point that partitions $overline{ab}$ in the ratio 3:7 is
(simplify your answer. type an ordered pair.)

Explanation:

Step1: Recall the section - formula

The formula to find the coordinates of a point \(P(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(A(-4,-7)\), \(B(12,5)\), \(m = 3\), and \(n = 7\).

Step2: Calculate the x - coordinate

\[

$$\begin{align*} x&=\frac{3\times12+7\times(-4)}{3 + 7}\\ &=\frac{36-28}{10}\\ &=\frac{8}{10}\\ &=\frac{4}{5}=0.8 \end{align*}$$

\]

Step3: Calculate the y - coordinate

\[

$$\begin{align*} y&=\frac{3\times5+7\times(-7)}{3 + 7}\\ &=\frac{15-49}{10}\\ &=\frac{-34}{10}\\ &=-\frac{17}{5}=-3.4 \end{align*}$$

\]

Answer:

\((0.8,-3.4)\)