Question

3 point x on $overline{jk}$ is $\frac{1}{3}$ of the distance from j to k. j(-1, 4) k(5, -3)

Explanation:

Step1: Use the section - formula

The section - formula for a point \(X(x,y)\) that divides the line segment joining \(J(x_1,y_1)\) and \(K(x_2,y_2)\) 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, \(m = 1\), \(n=2\), \(x_1=-1\), \(y_1 = 4\), \(x_2=5\), and \(y_2=-3\).

Step2: Calculate the x - coordinate of \(X\)

\[x=\frac{1\times5+2\times(-1)}{1 + 2}=\frac{5-2}{3}=\frac{3}{3}=1\]

Step3: Calculate the y - coordinate of \(X\)

\[y=\frac{1\times(-3)+2\times4}{1 + 2}=\frac{-3 + 8}{3}=\frac{5}{3}\]

Answer:

The coordinates of point \(X\) are \((1,\frac{5}{3})\)