Question

find the coordinates of point ( p ) along the directed line segment ( ab ) so that ( ap ) to ( pb ) is in the ratio 3 to 7. round your answer to the nearest tenth. coordinates: ( p (square,square) )

Explanation:

Step1: Use the section formula

If a point \(P(x,y)\) divides the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 3\), \(n = 7\), \(x_1=-2\), \(y_1 = 1\), \(x_2=4\), \(y_2 = 5\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\(x=\frac{3\times4+7\times(-2)}{3 + 7}=\frac{12-14}{10}=\frac{-2}{10}=-0.2\)

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\(y=\frac{3\times5+7\times1}{3 + 7}=\frac{15 + 7}{10}=\frac{22}{10}=2.2\)

Answer:

\(P(-0.2,2.2)\)