Question

Chapter 6:Coordinate Geometry
Given that A(6,8),B(p,-3) and C(-4,-6) are three points lying on a straight line such that AB:BC=m:n.Find
a)the ratio m:n
b)the value of p

Answer 1

@mathmath333

Answer 2

\(\large \color{black}{\begin{align}& \normalsize \text{For finding 'p' u need to equate the slope .}\hspace{.33em}\\~\\
&\normalsize \text{as the three points are collinear AB and BC should have same slope.}\hspace{.33em}\\~\\
&\dfrac{8-(-3)}{6-p}=\dfrac{-3-(-6)}{p-(-4)}
\end{align}}\)

Answer 3

okay

Answer 4

\(\large \color{black}{\begin{align} \normalsize \text{u can find m:n only after finding 'p'}\hspace{.33em}\\~\\

\end{align}}\)

Answer 5

\[p=-\frac{ 13 }{ 7 }\]

Answer 6

correct

Answer 7

For finding \(m:n\) u need the section formula

Answer 8

okay

Answer 9

\(\large \color{black}{\begin{align} x=\dfrac{nx_1+mx_2}{m+n}\hspace{.33em}\\~\\

\end{align}}\)

Answer 10

put the values and get the answer

Answer 11

\[-\frac{ 13 }{ 7 }=\frac{ 6n-4m }{ m+n }\]

Answer 12

\(A(6,8),B(p,-3) ~and~ C(-4,-6)\\
A(x_1,y_1),B(x,y)~and~C(x_2,y_2)\)

Answer 13

\[-\frac{ 13 }{ 7 }=\frac{ 6n-4m }{ m+n }\]

Answer 14

yea simplify it

Answer 15

\[-13m-13n=42n-28m\]

Answer 16

\[15m-55n=0\]@mathmath333

Answer 17

@mathmath333

Answer 18

Am i correct? @mathmath333

Answer 19

yes

Answer 20

what should we do next? @mathmath333

Answer 21

find \(\dfrac{m}{n}\)

Answer 22

i'm not sure how to do,can u show me pls?

Answer 23

\(\large \color{black}{\begin{align} 15m-55n=0\hspace{.33em}\\~\\
3m-11n=0\hspace{.33em}\\~\\
3m=11n\hspace{.33em}\\~\\
\dfrac{m}{n}=\dfrac{11}{3}

\end{align}}\)

Answer 24

Thank you @mathmath333 :)