First slide

Cartesian plane

Question

If the intercept made on the line $y = mx$ by lines $y = 2$ and $y = 6$ is less than 5, then the range of values of m is

Moderate

A

$(- \infty, - 4 / 3) \cup (4 / 3, + \infty)$
B

$(- 4 / 3, 4 / 3)$
C

$(- 3 / 4, 4 / 3)$
D

none of these

Solution

The distance between $(2 / m, 2)$ and $(6 / m, 6)$ is less than 5.
Hence,
${(\frac{2}{m} - \frac{6}{m})}^{2} + {(2 - 6)}^{2} < 25$
or $\frac{16}{m^{2}} < 9$
or $m^{2} > \frac{16}{9}$
i,e., $m > \frac{4}{3} or m < \frac{- 4}{3}$

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