Question

find the coordinates of the point $\frac{7}{10}$ of the way from a to b. the coordinates of the point $\frac{7}{10}$ of the way from a to b are . (type an ordered pair.)

Explanation:

Step1: Identify the coordinates of A and B

Let \(A(- 2,-8)\) and \(B(14,6)\).

Step2: Use the section - formula for x - coordinate

The formula for the x - coordinate of a point that divides the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here \(m = 7\), \(n=3\), \(x_1=-2\), \(x_2 = 14\). So \(x=\frac{7\times14+3\times(-2)}{7 + 3}=\frac{98 - 6}{10}=\frac{92}{10}=9.2\).

Step3: Use the section - formula for y - coordinate

The formula for the y - coordinate of a point that divides the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 7\), \(n = 3\), \(y_1=-8\), \(y_2=6\). So \(y=\frac{7\times6+3\times(-8)}{7 + 3}=\frac{42-24}{10}=\frac{18}{10}=1.8\).

Answer:

\((9.2,1.8)\)