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 the coordinates of A and B

A(-3,-7), B(12,5)

Step2: Use the section - formula for x - coordinate

If a point P divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), the x - coordinate of P is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(m = 3\), \(n=7\), \(x_1=-3\), \(x_2 = 12\). So \(x=\frac{3\times12+7\times(-3)}{3 + 7}=\frac{36-21}{10}=\frac{15}{10}=1.5\)

Step3: Use the section - formula for y - coordinate

The y - coordinate of P is \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 3\), \(n = 7\), \(y_1=-7\), \(y_2 = 5\). So \(y=\frac{3\times5+7\times(-7)}{3 + 7}=\frac{15-49}{10}=\frac{-34}{10}=-3.4\)

Answer:

\((1.5,-3.4)\)