Question

point l lies on (overline{jk}) such that (jl:kl) is 3:4. graph l.

Explanation:

1. First, assume the coordinates of point \(J=(4,8)\) and point \(K=(12,1)\) (by observing the graph).

• The section - formula for a point \(L(x,y)\) 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, \(m = 3\) and \(n = 4\), \(x_1 = 4\), \(y_1 = 8\), \(x_2 = 12\), \(y_2 = 1\).

1. Calculate the \(x\) - coordinate of point \(L\):

• \(x=\frac{3\times12 + 4\times4}{3 + 4}=\frac{36+16}{7}=\frac{52}{7}\approx7.43\).

1. Calculate the \(y\) - coordinate of point \(L\):

• \(y=\frac{3\times1+4\times8}{3 + 4}=\frac{3 + 32}{7}=\frac{35}{7}=5\).

Step1: Identify the section - formula

Use \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\) for a point \(L\) dividing \(JK\) in ratio \(m:n\).

Step2: Substitute values for \(x\) - coordinate

Substitute \(m = 3\), \(n = 4\), \(x_1 = 4\), \(x_2 = 12\) into \(x=\frac{mx_2+nx_1}{m + n}\) to get \(x=\frac{3\times12 + 4\times4}{3 + 4}\).

Step3: Substitute values for \(y\) - coordinate

Substitute \(m = 3\), \(n = 4\), \(y_1 = 8\), \(y_2 = 1\) into \(y=\frac{my_2+ny_1}{m + n}\) to get \(y=\frac{3\times1+4\times8}{3 + 4}\).

Answer:

The coordinates of point \(L\) are \((\frac{52}{7},5)\approx(7.43,5)\). Graph the point \(L\) on the grid at approximately \(x = 7.43\) and \(y = 5\).