Question

point n lies on (overline{lm}) such that (ln:nm) is (2:1). graph n.

Explanation:

Step1: Find coordinates of L and M

From the graph, \( L=(4,15) \) and \( M=(7,12) \) (assuming each grid is 1 unit, checking the x and y positions: L is at x=4, y=15; M is at x=7, y=12).

Step2: Use section formula (internal division)

The section formula for a point \( N(x,y) \) dividing the line segment joining \( (x_1,y_1) \) and \( (x_2,y_2) \) in the ratio \( m:n \) is \( x=\frac{mx_2 + nx_1}{m + n} \), \( y=\frac{my_2 + ny_1}{m + n} \). Here, \( m = 2 \), \( n = 1 \), \( (x_1,y_1)=(4,15) \), \( (x_2,y_2)=(7,12) \).

Step3: Calculate x-coordinate of N

\( x=\frac{2\times7 + 1\times4}{2 + 1}=\frac{14 + 4}{3}=\frac{18}{3}=6 \)

Step4: Calculate y-coordinate of N

\( y=\frac{2\times12 + 1\times15}{2 + 1}=\frac{24 + 15}{3}=\frac{39}{3}=13 \)

So, the coordinates of \( N \) are \( (6,13) \). To graph \( N \), plot the point at x=6, y=13 on the grid.

Answer:

The coordinates of point \( N \) are \( (6, 13) \), and it should be graphed at the intersection of \( x = 6 \) and \( y = 13 \) on the given grid.