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In the xy coordinate plane, does the point (3,4) lie on line

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In the xy coordinate plane, does the point (3,4) lie on line [#permalink] New post 15 Apr 2013, 04:03
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In the xy coordinate plane, does the point (3,4) lie on line t?

(1) The line 5y-45=-x is perpendicular to the line t.

(2) The line with the equation y= \frac{3}{4}x - 11 intersects the line t when y=-11.

Please show a step by step approach here and explain why it is not
[Reveal] Spoiler:
A
. I do not understand the official explanation.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Apr 2013, 04:07, edited 1 time in total.
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Re: In the [m]xy[/m] coordinate plane, does the point (3,4) lie [#permalink] New post 15 Apr 2013, 04:09
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y=mx+q the question is: 4=m3+q?

1) The line 5y-45=-x is perpendicular to the line t.
y=-\frac{1}{5}x+9 those are perpendicular so m=5. is 3m+q=3*5+q=4? it depends on q. Not sufficient

2) The line with the equation y= \frac{3}{4}x - 11 intersects the line t when y=-11.
-11=\frac{3}{4}x-11 x=0 y=-11 is where those lines intersect, but this point defines the intersenction of t with the y-axis => defines q.
Is 3m-11=3? it depends on m. Not sufficient

1+2) We have m and q. Sufficient to say if 4=5*3-11. So the answer is YES
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Re: In the xy coordinate plane, does the point (3,4) lie on line [#permalink] New post 15 Apr 2013, 04:21
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In the xy coordinate plane, does the point (3,4) lie on line t?

Minimum calculations are needed to answer this question. Even the calculations below are not necessary and are just to illustrate.

(1) The line 5y-45=-x is perpendicular to the line t. Given that line y=9-x/5 (5y-45=-x) is perpendicular to the line t means that the slope of line t is 5 (negative reciprocal of the slope of line y=9-x/5, which is -1/5). Now, line with the slope of 5 may or may not pass through point (3,4). For example, y=5x-11 (YES) and y=5x (NO). Not sufficient.

(2) The line with the equation y= \frac{3}{4}x - 11 intersects the line t when y=-11 --> -11= \frac{3}{4}x - 11 --> x=0. So, we have that line t passes through point (0, -11). Obviously this line may also pass through (3,4) but may as well not. Not sufficient.

(1)+(2) We know the slope of line t and point (0, -11) it passes, which is enough to get its equation. Therefore we can determine whether it passes point (3,4). Sufficient.

Answer: C.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In the xy coordinate plane, does the point (3,4) lie on line   [#permalink] 15 Apr 2013, 04:21
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In the xy coordinate plane, does the point (3,4) lie on line

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