Question

The ratio in which the line segment joining
the points (-6, 10) and B(3,-8) is divided by -
4,6)
A. (7:2)
B. (6:3)
C. (3:6)
D. (2:7)​

Answer 1

Answer:

i hope c no.

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Answer 2

GIVEN :-

• segment joining the points are :- (-6, 10) and B(3,-8) is divided by (-4, 6)

TO FIND :-

• The ratio in which the line segment joining

SOLUTION :-

let the ratio = m : n

hence ,

$\implies \rm{ \bold {a \: ( - 6 ,1)≡(x _{1}, \:y _{1})}}$

$\implies \rm{ \bold {b\: ( 3 , - 8)≡(x _{2}, \:y _{2})}}$

$\implies \rm{ \bold {c\: ( - 4 \: , 6)≡(x _{3}, \:y _{3})}}$

now we know the section formula that ,

$\implies \boxed{\rm { \dfrac{mx _{2} + \: nx _{1}}{m + n}, \dfrac{my_{2} + \: ny _{1}}{m + n} = (x _{3}, \:y _{3})}}$

$\implies \rm { \dfrac{mx _{2} + \: nx _{1}}{m + n}, \dfrac{my_{2} + \: ny _{1}}{m + n} = ( - 4 \: , \:6)}$

we can solve by both by ‘ X ’ or ‘ y ’ so we are take X

$\implies \rm { \dfrac{mx _{2} + \: nx _{1}}{m + n}= - 4 \: }$

$\implies \rm { mx _{2} + \: nx _{1} = - 4 \: (m + n)\: }$

now put the value of X2 and X1 in the following

$\implies \rm { m(3) + \: n( - 6) = - 4 \: (m + n)\: }$

$\implies \rm { 3m - 6n = - 4 m - 4 n\: }$

$\implies \rm { 3m + 4m = 6n - 4 n\: }$

$\implies \rm { 7m = 2 n\: }$

$\implies \rm { \dfrac{m}{n} = \: \dfrac{2}{7} }$

$\implies \boxed{ \boxed { \rm { m : n = 2 : 7 }}}$

OTHER INFORMATION :-

Section Formula :

• When a point C divides a segment AB in the ratio m:n, we use the section formula to find the coordinates of that point. The section formula has 2 types. These types depend on the position of point C. It can be present between the 2 points or outside the segment.

The two types are:

• Internal Section Formula

• External Section Formula

Internal Section Formula

• Also known as the Section Formula for Internal Division. When the line segment is divided internally in the ration m:n, we use this formula. That is when the point C lies somewhere between the points A and B.