5m - 12 - 2m + 6 + 3m

Mathematics

1 answer:

lapo4ka [179]3 years ago

6 0

Answer:

6(m-1)

Step-by-step explanation:

See Image Below:)

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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).

QveST [7]

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

$\begin{gathered} RP:PS \\ \Rightarrow\frac{1}{3}:\frac{2}{3} \\ thus,\text{ we have} \\ 1:2 \end{gathered}$

Using the section formula expressed as

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

In this case,

$\begin{gathered} m=1 \\ n=2 \end{gathered}$

where

$\begin{gathered} x_1=-7 \\ y_1=-2 \\ x_2=2 \\ y_2=4 \end{gathered}$

Thus, by substitution, we have

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

Hence, the y-coordinate of the point P is