Question

For the line segment whose endpoints are L (0, 1) and M (2,8), find the y coordinate for the point located 3/5 the distance from L to M
5.2
3.5
4.8
1.6

Answer 1

Answer:

$5.2$.

Step-by-step explanation:

The question states that this point is on segment $LM$, with the distance between this point and $L\!$ being $(3/5)$ the distance between $L$ to $M$.

It could be shown (using a pair of similar right triangles) that the $(3/5)$ ratio applies not only to the (sloped) distance between this point and $L$, but to the vertical distance as well.

The vertical distance between this point and $L\!$ would also be $(3/5)$ the vertical distance between $\! L$ and $M$.

The vertical distance between $\! L$ and $M$ is the difference between their $y$ coordinates, $8 - 1 = 7$.

The vertical distance between this point and $L$ would be $(3/5)$ of the vertical distance between $L\!$ and $M\!$, $7 \times (3/5) = 21/5$.

Since $M\!$ is above $L\!$, any point on the segment between these two points would also be above $L$. Add the vertical distance between $\! L$ and the requested point to the $y$ coordinate of $L\!\!$ to find the $y\!$ coordinate of the requested point: $(21/5) + 1 = 26/5 = 5.2$.