Question

find the coordinates of the point that is $\frac{7}{10}$ from a to b. (type your answer as an ordered pair in parenthesis with no spaces)

Explanation:

Step1: Identify the coordinates of A and B

Let \(A=(0, - 8)\) and \(B=(10,6)\). The section - formula for 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 given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 7\) and \(n=10 - 7=3\), \(x_1 = 0\), \(y_1=-8\), \(x_2 = 10\), \(y_2 = 6\).

Step2: Calculate the x - coordinate of the point

\[x=\frac{7\times10+3\times0}{7 + 3}=\frac{70+0}{10}=7\]

Step3: Calculate the y - coordinate of the point

\[y=\frac{7\times6+3\times(-8)}{7 + 3}=\frac{42-24}{10}=\frac{18}{10}=1.8\]

Answer:

(7,1.8)