The straight lines L1 and L2 pass through the origin and trisect the line segment of the line L : 9x + 5y = 45 between the axes. If m1 and m2 are the slopes of the lines L1 and L2 then the point of intersection of the line y = (m1 + m2)x with L lies on

Engineering

Mathematics

Various Form of a Straight Line

Question

The straight lines L₁ and L₂ pass through the origin and trisect the line segment of the line L : 9x + 5y = 45 between the axes. If m₁ and m₂ are the slopes of the lines L₁ and L₂ then the point of intersection of the line y = (m₁ + m₂)x with L lies on

A

6x + y = 10

B

6x – y = 15

C

y – x = 5

D

y – 2x = 15

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m₁ = $\frac{3}{(10 / 3)} = \frac{9}{10}$

m₂ = $\frac{6}{(5 / 3)} = \frac{18}{5}$

m₁ + m₂ = $\frac{9 + 36}{10} = \frac{45}{10} = \frac{9}{2}$

So, y = (m₁ + m₂) x is y = $\frac{9}{2} x$

Now solving y = $\frac{9}{2} x$ and 9x + 5y = 45

$\Rightarrow 2 y + 5 y = 45 \Rightarrow y = \frac{45}{7}, x = \frac{10}{7}$

y – x = $\frac{35}{7} = 5$ .

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