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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]

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Updated on: 15 Apr 2013, 05:07
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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 . I do not understand the official explanation.

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Originally posted by obs23 on 15 Apr 2013, 05:03.
Last edited by Bunuel on 15 Apr 2013, 05:07, edited 1 time in total.
Edited the question.
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Re: In the xy coordinate plane, does the point (3,4) lie on line  [#permalink]

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15 Apr 2013, 05:21
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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.

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

Hope it helps.
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Re: In the [m]xy[/m] coordinate plane, does the point (3,4) lie  [#permalink]

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15 Apr 2013, 05:09
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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]

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12 Aug 2016, 23:23
obs23 wrote:
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 . I do not understand the official explanation.

Keep in mind, there are two ways in which you can define a line t:
- You are given two distinct points that lie on that line. You join the two points and you have a defined line.
- You are given one point and the slope of the line. You make a line with the given slope on the point.

Question: In the xy coordinate plane, does the point (3,4) lie on line t?
You need to define line t to figure out if a point lies on it.

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

This gives you the slope of line t but you don't have any point on it. So you cannot define line t.
Not sufficient.

(2) The line with the equation $$y= \frac{3}{4}x - 11$$ intersects the line t when y=-11.
When y = -11, you can find the value of co-ordinate x by plugging in $$y= \frac{3}{4}x - 11$$.
So you will have a point which lies on line t. But you don't have another point.
Hence you cannot define line t using this statement alone.

Using both stmnts, you get the slope of line t and a point that lies on it. This will help you define t uniquely. So you will be able to find out whether (3, 4) lies on it.
Sufficient.

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Re: In the xy coordinate plane, does the point (3,4) lie on line  [#permalink]

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15 Apr 2019, 07:52
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Re: In the xy coordinate plane, does the point (3,4) lie on line   [#permalink] 15 Apr 2019, 07:52
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