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Find the Y-coordinate of point P that lies 1/3 along segment RS, where R (-7, -2) and S (2, 4).

Sagot :

Solution:

Given that the point P lies 1/3 along the segment RS as shown below:

To find the y coordinate of the point P, since the point P lies on 1/3 along the segment RS, we have

[tex]\begin{gathered} RP:PS \\ \Rightarrow\frac{1}{3}:\frac{2}{3} \\ thus,\text{ we have} \\ 1:2 \end{gathered}[/tex]

Using the section formula expressed as

[tex][\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}][/tex]

In this case,

[tex]\begin{gathered} m=1 \\ n=2 \end{gathered}[/tex]

where

[tex]\begin{gathered} x_1=-7 \\ y_1=-2 \\ x_2=2 \\ y_2=4 \end{gathered}[/tex]

Thus, by substitution, we have

[tex]\begin{gathered} [\frac{1(2)+2(-7)}{1+2},\frac{1(4)+2(-2)}{1+2}] \\ \Rightarrow[\frac{2-14}{3},\frac{4-4}{3}] \\ =[-4,\text{ 0\rbrack} \end{gathered}[/tex]

Hence, the y-coordinate of the point P is

[tex]0[/tex]

View image MiliahW785963
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