in proportion -navin drives his car at a constant speed.if he travels 8km in 10 minutes,how long will he take to travel 32 km
Answers
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+n
mx
2
+nx
1
,
mn
my
2
+ny
1
)
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+n
m(6)+n(−3)
,
m+n
m(−8)+n(10)
)
⟹(−1,6)=(
m+n
6m−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+n
6m−3n
⟹−m−n=6m−3n
⟹−n+3n=6m+m
⟹2n=7m
⟹
7
2
×n=m
⟹
7
2
=
n
m
⟹
m:n=2:7
Step-by-step explanation:
♥️♥️♥️♥️