Question

point l lies on (overleftrightarrow{jk}) such that (jl:kl) is (5:1). graph l.

Explanation:

Step1: Find coordinates of J and K

From the graph, \( J(-5, 1) \) (wait, no, looking at the grid: J is at (-5, 1)? Wait, no, the x-axis: J is at x=-5? Wait, the grid lines: J is at (-5, 1)? Wait, no, let's check again. Wait, the x-coordinate: J is at x=-5? Wait, the graph: J is at (-5, 1)? Wait, no, looking at the points: J is at (-5, 1)? Wait, no, the x-axis: from -10 to 10, each grid is 1 unit. J is at (-5, 1)? Wait, no, the point J: looking at the graph, J is at (-5, 1)? Wait, no, maybe J is at (-5, 1)? Wait, no, let's see: the x-coordinate of J: between -6 and -4, so x=-5, y=1? Wait, no, the y-coordinate: J is at y=1? Wait, the line JK: J is at (-5, 1)? Wait, no, maybe I misread. Wait, K is at (7, -5)? Wait, no, the graph: K is at (7, -5)? Wait, no, the point K is at (7, -5)? Wait, no, looking at the grid, K is at (7, -5)? Wait, no, the y-coordinate of K is -5? Wait, the grid: from -10 to 10, y-axis. K is at (7, -5)? Wait, no, the original graph: J is at (-5, 1)? Wait, no, let's check again. Wait, J is at (-5, 1)? Wait, no, the x-axis: J is at x=-5, y=1. K is at (7, -5). Wait, let's confirm:

Wait, the x-coordinate of J: the grid lines, J is at x=-5 (since between -6 and -4, so x=-5), y=1 (since between 0 and 2, y=1). K is at x=7, y=-5 (between -6 and -4, y=-5? Wait, no, K is at (7, -5)? Wait, the point K is at (7, -5)? Let's check the line: from J(-5,1) to K(7,-5).

Step2: Use section formula

The section formula for a point L dividing JK in the ratio \( m:n = 5:1 \) (JL:KL = 5:1, so L is closer to K? Wait, no: JL:KL = 5:1, so J---L---K, with JL = 5 parts, KL = 1 part. So the ratio m:n where m is the part from J to L, n from L to K. So the coordinates of L are given by:

\( x = \frac{m \cdot x_K + n \cdot x_J}{m + n} \), \( y = \frac{m \cdot y_K + n \cdot y_J}{m + n} \)

Here, m = 5, n = 1, \( x_J = -5 \), \( y_J = 1 \), \( x_K = 7 \), \( y_K = -5 \)

Step3: Calculate x-coordinate of L

\( x = \frac{5 \cdot 7 + 1 \cdot (-5)}{5 + 1} = \frac{35 - 5}{6} = \frac{30}{6} = 5 \)

Step4: Calculate y-coordinate of L

\( y = \frac{5 \cdot (-5) + 1 \cdot 1}{5 + 1} = \frac{-25 + 1}{6} = \frac{-24}{6} = -4 \)

So the coordinates of L are (5, -4). To graph L, plot the point (5, -4) on the grid.

Answer:

The coordinates of point \( L \) are \( (5, -4) \), so graph the point at \( (5, -4) \) on the coordinate plane.