Question

In the figure below K lies between J and L. Find the location of K so that the ratio of JK to KL is 4 to 1 J=-27 and L=3 K=?

Answer 1

well, firstly hmmm we know btw you're missing the picture, but anyhow, we have the coordinates and I assume is on a number line, so hmmm we have J at -27 and L at 3, on a number line from -27 to 0 is hmmm well 27 units total :), and from 0 to 3 is 3 units, sum them up for a total of 27 + 3 = 30 units, so the distance from -27 to 3 is 30 units.

Now, let's divide that whole of 30 units by (4 + 1), and then we'll distribute accordingly to get the 4 : 1 ratio needed, so

`\cfrac{30}{4+1}\implies \cfrac{30}{5}\implies 6 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{JK}{4}~~ : ~~\stackrel{KL}{1}\implies \cfrac{JK}{KL}=\cfrac{4}{1}\implies \cfrac{JK}{KL}=\cfrac{4(6)}{1(6)}\implies \cfrac{JK}{KL}=\cfrac{24}{6}`

what does that all mean?

well, it means that JK has 24 units, and since J is at -27, if we move 24 units to the right, we'll end up at -3, so K is at -3, or K = -3.

Now, we could have used KL of 6 units and K would have been the same.

`\stackrel{ J }{\boxed{-27}}\rule[0.35em]{17em}{0.25pt}\stackrel{\textit{\LARGE K} }{\boxed{-3}}\rule[0.35em]{5em}{0.25pt}\stackrel{ L }{\boxed{3}}`