Question

question 6 of 10
in line segment ab with endpoints a(1,6) and b(16, - 14), the point p divides ab in a ratio of 3:2 from point a.
determine the coordinates of point p.

Explanation:

Step1: Recall section - formula for x - coordinate

The formula for the x - coordinate 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 \(m:n\) from point \(A\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1 = 1\), \(x_2=16\), \(m = 3\), and \(n = 2\).
\[x=\frac{3\times16+2\times1}{3 + 2}\]
\[x=\frac{48 + 2}{5}=\frac{50}{5}=10\]

Step2: Recall section - formula for y - coordinate

The formula for the y - coordinate 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 \(m:n\) from point \(A\) is \(y=\frac{my_2+ny_1}{m + n}\). Here, \(y_1 = 6\), \(y_2=-14\), \(m = 3\), and \(n = 2\).
\[y=\frac{3\times(-14)+2\times6}{3 + 2}\]
\[y=\frac{-42 + 12}{5}=\frac{-30}{5}=-6\]

Answer:

\((10,-6)\)