Questions: The point K lies on the segment JL. Find the coordinates of K so that JK is 1/4 of JL.

Transcript text: The point $K$ lies on the segment $\overline{J L}$. Find the coordinates of $K$ so that $J K$ is $\frac{1}{4}$ of $J L$.

Solution

Solution Steps

Step 1: Find the ratio

The problem states that JK is (1/4) of JL. This means that the ratio of JK to JL is 1:4. Alternatively, the ratio of JK to KL is 1:3.

Step 2: Apply the section formula

The section formula for finding a point dividing a line segment in a given ratio is: If a point K divides the line segment joining points J(x1, y1) and L(x2, y2) in the ratio m:n, then the coordinates of K are given by: K = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Here, J(-28, 22), L(4, -2), and the ratio JK:KL is 1:3, so m=1 and n=3.

Step 3: Calculate the x-coordinate of K

x-coordinate of K = (1 * 4 + 3 * (-28))/(1+3) = (4 - 84)/4 = -80/4 = -20

Step 4: Calculate the y-coordinate of K

y-coordinate of K = (1 * (-2) + 3 * 22)/(1+3) = (-2 + 66)/4 = 64/4 = 16