Question

Determine the ratio in which the point p( m, 6 ) divides the join of A( - 4, 3 ) and B( 2, 8 ). Also Find the value of m.

Answer 1

Answer:

m = -2/5

Step-by-step explanation:

Answer is explained below.

Ratio m = -2/5

Answer 2

Hey there !!


Let the required ratio be k : 1 .

Here,
$x_1 = - 4 , \: y _1 = 3 , \: x _2 = 2 \: \: and \: \: y _2 = 8.$

[ Using section formula :- ]

Then, coordinates of p are

$( \frac{mx _2 + n x_1}{m + n} , \frac{my _2 + n y_1}{m + n}) \\ \\ = ( \frac{2k - 4}{k + 1} , \frac{8k + 3}{k+ 1}). \\ \\ \therefore \frac{8k + 3}{k+ 1} = 6. \\ \\ \implies 8k + 3 = 6k + 6. \\ \\ = > 8k - 6k = 6 - 3. \\ \\ = > 2k = 3. \\ \\ = > k = \frac{3}{2} .$

So, the required ratio is $\frac{3}{2}$ : 1 .

Or 3 : 2 . [ = 3/2 : 1 = 3 : 2 × 1 = 3 : 2 ] .


$\therefore m = \frac{2k - 4}{k + 1} \\ \\ = \frac{(2 \times \frac{3}{2} - 4) }{( \frac{3}{2} + 1)} \\ \\ = \frac{3 - 4}{ \frac{3 + 2}{2} } . \\ \\ = \frac{ - 1 \times 2}{5} . \\ \\ \huge \red{ \boxed{ = \frac{ - 2}{5} . }}$



✔✔ Hence, it is solved ✅✅



THANKS



#BeBrainly.