Question

40. Find two parts
41. Find the ratio in which the line segment joining the points (-3, 10) and (6,-8)
is divided by (-1, 6).
​

Answer 1

Answer:

Answer:-

Given:-

( - 1 , 6) divided the line segment joining the points ( - 3 , 10) & (6 , - 8).

Let , the ratio in which the line segment divided be m : n.

Using section formula;

i.e.,

The co - ordinates of a point divided the line segment joining the points (x₁ , y₁) & (x₂ , y₂) in the ratio m : n are;

\boxed {\sf \: (x \: ,\: y) = \bigg( \dfrac{mx_2 + nx_1}{m + n} \: \: ,\: \: \dfrac{my_2 + ny_1}{mn} \bigg)}(x,y)=(m+nmx2+nx1,mnmy2+ny1)

Let,

x = - 1

y = 6

x₁ = - 3

y₁ = 10

x₂ = 6

y₂ = - 8

Hence,

\begin{gathered} \implies \sf \: ( - 1 \: , \: 6) = \bigg( \frac{m(6) + n( - 3)}{m + n} \: \: ,\: \: \frac{m( - 8) + n(10)}{m + n} \bigg) \\ \\ \\ \implies \sf \: ( - 1 \: , \: 6) = \bigg( \frac{6m - 3n}{m + n} \: \: ,\: \: \frac{ - 8m+ 10n}{m + n} \bigg) \\ \\ \end{gathered}⟹(−1,6)=(m+nm(6)+n(−3),m+nm(−8)+n(10))⟹(−1,6)=(m+n6m−3n,m+n−8m+10n)

On comparing both sides we get;

\begin{gathered} \implies \sf \: - 1 = \frac{6m - 3n}{m + n} \\ \\ \\ \implies \sf \: - m - n = 6m - 3n \\ \\ \\ \implies \sf \: - n + 3n = 6m + m \\ \\ \\ \implies \sf \:2n = 7m \\ \\ \\ \implies \sf \: \frac{2}{7} \times n = m \\ \\ \\ \implies \sf \: \frac{2}{7} = \frac{m}{n} \\ \\ \\ \implies \boxed{\sf \:m :n = 2 : 7}\end{gathered}⟹−1=m+n6m−3n⟹−m−n=6m−3n⟹−n+3n=6m+m⟹2n=7m⟹72×n=m⟹72=nm⟹m:n=2:7

∴ The ratio in which the line segment is divided is 2 : 7.