Parastoobahramidn
Answered

IDNLearn.com makes it easy to find the right answers to your questions. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.

find the equation of the line that passes through P(7,20) and Q the midpoint of R (-3,5) and S (5,11)

Sagot :

Homeworksupportidn
First we have to find midpoint of R and S.
We can use formula such for it.[tex]Qx= \frac{Rx+Sx}{2}[/tex] and [tex]Qy= \frac{Ry+Sy}{2}[/tex].
We obtained coordinates of point Q 
[tex]Qx= \frac{-3+5}{2}=1[/tex] and [tex]Qy= \frac{5+11}{2}=8 [/tex]

Now, we can find the line equation using formula y=ax+b. 
We can substitute coordinates of P and Q to this formula and solving system of equation get the answer.

After substituting we obtaind such system
[tex]\left \{ {{20=7a+b } \atop {8=a+b}} \right. [/tex]

From the system of equation we obtain result
[tex] \left \{ {{a=2} \atop {b=6}} \right. [/tex] 

Now we can put our resuts to general line equation.
[tex]y=2x+6[/tex]
Lilithidn
[tex] R (-3,5), \ \ \ S (5,11) \ midpoint \ of \ R \ and \ S \\ \\ Midpoint \ Formula \\\\(x,y)= \left ( \frac{x_{1}+x_{2}}{2},\frac {{}y_{1}+y_{2}}{2} \right ) \\ \\Q= \left ( \frac {-3+5}{2},\frac { 5+11}{2} \right ) \\ \\Q= \left ( \frac {2}{2},\frac { 16}{2} \right ) \\ \\Q= \left ( 1 ,8) \right )[/tex]

[tex] the \ equation \ of \ the \ line \ that \ passes \ through \ P(7,20) \ and \ Q (1,8)\\\\First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} } \\ \\m=\frac{ 8-20}{1-7 } =\frac{-12}{-6}=2\\\\the \ slope \ intercept \ form \ is : \\ \\ y= mx +b \\\\20=2\cdot 7+b \\\\20=14+b\\\\b=20-14\\b=6\\\\y=2x+6[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.