Question

for the line segment whose endpoints are l (0, 1) and m (2, 8), find the y coordinate for the point located \\(\frac{3}{5}\\) the distance from l to m. (4 points)
5.2
3.5
4.8
1.6

Explanation:

Step1: Recall the section formula for y - coordinate

The section formula for the y - coordinate of a point that divides the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(y = y_1+\frac{m}{m + n}(y_2 - y_1)\). Here, the point is \(\frac{3}{5}\) of the distance from \(L(0,1)\) to \(M(2,8)\), so the ratio \(m:n=3:2\) (because if the distance from \(L\) to the point is \(\frac{3}{5}\) of \(LM\), then the distance from the point to \(M\) is \(1-\frac{3}{5}=\frac{2}{5}\) of \(LM\), so \(m = 3\), \(n = 2\)), \(y_1=1\), \(y_2 = 8\).

Step2: Substitute the values into the formula

Substitute \(y_1 = 1\), \(m = 3\), \(n = 2\), \(y_2=8\) into the formula \(y=y_1+\frac{m}{m + n}(y_2 - y_1)\)
\[

$$\begin{align*} y&=1+\frac{3}{3 + 2}(8 - 1)\\ &=1+\frac{3}{5}\times7\\ &=1+\frac{21}{5}\\ &=1 + 4.2\\ &=5.2 \end{align*}$$

\]

Answer:

5.2