Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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]
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]
[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]
[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]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.