Question

find the ratio (-3,5) ; (6,4) is divided by (-1,6) class 10th​

Answer 1

Answer:-

Given:

( - 1 , 6) divides the line segment joining the points ( - 3 , 5) & (6 , 4).

using section formula;

i.e., the co - ordinates of a point which divides the line segment joining the points (x₁ , y₁) , (x₂ , y₂) internally in the ratio m : n are:

$\sf \: (x \: , \: y) = \bigg( \dfrac{mx _{2} + nx _{1} }{m + n} \: \: ,\: \: \dfrac{my _{2} + ny _{1} }{m + n} \bigg)$

Let,

• x₁ = - 3

• x₂ = 6

• y₁ = 5

• y₂ = 4

• x = - 1

• y = 6

• m = m

• n = n.

Hence,

$\implies \sf \: (x \:, \: y) = \bigg( \dfrac{m( 6) + n( - 3)}{m + n} \: \: , \: \: \dfrac{m(4) + n(5)}{m + n} \bigg) \\ \\ \implies \sf \:( - 1 \: , \: 6) = \bigg( \frac{6m - 3n}{m + n} \: \: , \: \: \frac{4m + 5n}{m + n} \bigg) \\ \\ \implies \sf \: - 1 = \frac{6m - 3n}{m + n} \\ \\ \implies \sf \: - 1(m + n) = 6m - 3n \\ \\ \implies \sf \: - m - n = 6m - 3n \\ \\ \implies \sf \: \: - m - 6m = - 3n + n \\ \\ \implies \sf \: - 7m = - 2n \\ \\ \implies \sf \: \frac{ - 7 \times m}{ - 2 \times n} = 1 \\ \\ \implies \sf \red{ \frac{m}{n} = \frac{2}{7} }$

⟹ m : n = 2 : 7.

Therefore, the ratio in which the point divides is 2 : 7.