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05 Jan 2010, 08:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:15) correct
22%
(01:25)
wrong
based on 439
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In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?
(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
26 Sep 2010, 12:19
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udaymathapati
Line \(l\) passes through the point (16/5, 12/5). If we knew some other point through which line \(l\) passes then we would be able to calculate the slope: the slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.
(1) The product of the slopes of line \(l\) and line \(k\) is -1 --> line \(l\) and \(k\) are perpendicular to each other (the two lines are perpendicular if and only the product of their slopes is -1). Not, sufficient, as we can have infinite # of perpendicular lines passing through some point (16/5, 12/5).
(2) Line \(k\) passes through the origin --> we have the second point for line \(k\), so we can calculate the slope of \(k\), but we don't know the relationship between the lines \(l\) and \(k\). Not sufficient.
(1)+(2) We can calculate the slope of \(k\) and we know that the product of the slopes of \(l\) and \(k\) is -1, so we can calculate the slope of line \(l\) too. Sufficient.
Answer: C.
For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).
Hope it helps.
General Discussion
05 Jan 2010, 08:14
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C..
si) gives us the relation in two lines ..the two r perpendicular to each other...not suff
sii) it gives us the 2nd pt on line k... we can find the slope of k from it but not l.. not suff.
combined frm k ,slope of l can be found frm reln in si..suff
si) gives us the relation in two lines ..the two r perpendicular to each other...not suff
sii) it gives us the 2nd pt on line k... we can find the slope of k from it but not l.. not suff.
combined frm k ,slope of l can be found frm reln in si..suff
