Question

point p is located on mn where pn = 1/4 mn. what are the coordinates of point p? enter the answer in the boxes in decimal form. use * for the decimal.

Explanation:

Step1: Find the coordinates of \(M\) and \(N\)

From the graph, \(M(-2,6)\) and \(N(5,-1)\)

Step2: Use the section formula

If a point \(P(x,y)\) divides the line - segment joining \(M(x_1,y_1)\) and \(N(x_2,y_2)\) such that \(PN=\frac{1}{4}MN\), then \(MP:PN = 3:1\)
The section formula for a point \(P(x,y)\) that divides the line - segment joining \(M(x_1,y_1)\) and \(N(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\)
Here \(m = 3\), \(n = 1\), \(x_1=-2\), \(y_1 = 6\), \(x_2=5\), \(y_2=-1\)

Calculate \(x\) - coordinate

\(x=\frac{3\times5+1\times(-2)}{3 + 1}=\frac{15-2}{4}=\frac{13}{4}=3.25\)

Calculate \(y\) - coordinate

\(y=\frac{3\times(-1)+1\times6}{3 + 1}=\frac{-3 + 6}{4}=\frac{3}{4}=0.75\)

Answer:

\((3.25,0.75)\)