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In the rectangular coordinate system, lines m and n intersec

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In the rectangular coordinate system, lines m and n intersec

by Vincen » Sat Nov 30, 2019 7:52 am
In the rectangular coordinate system, lines \(m\) and \(n\) intersect at the origin. Is line \(m\) perpendicular to line \(n?\)

(1) Line \(n\) passes through the point \( (-a, -a) \), where \(a\ne 0\), and line \(m\) has a slope of \(-1\).

(2) The product of the slope of line \(m\) and the slope of line \(n\) is \(-1\).

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT
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Source: — Data Sufficiency |
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by nitink » Tue Dec 03, 2019 11:56 am
The lines will be perpendicular to each other when The product of the slope of line m and the slope of line n is -1.

From 1, slope of N = 0 - (-a) / 0 - (-a) = 1
Slope of M = -1

Product = -1
Hence sufficient

From 2, Product of slopes = -1

So Sufficient.

So answer is D.
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