Sorry i am not able to absorb this

frank1 wrote:Well,
i just took manhattan CAT3 today 16th dec 2010
This was one of my mistakes
Does line S intersect line segment QR?

(1) The equation of line S is y = -x + 4.

(2) The slope of line S is -1.
Fig Below

Official answer is A

BUT

My answer was D
A clearly satifies the thing

For B ,S has same slope as the line joining two points so it is parallel
parallel lines never intersect each other
so answer is NO
SUFFICIENT
So it should be D
BUT
manhattan says
For B
INSUFFICIENT: Line S has the same slope as line segment QR, so they are parallel. They might intersect; for example, if Line S passes through points Q and R. But they might never intersect; for example, if Line S passes above or below line segment QR.


The correct answer is A.

so whats problem with my logic.To be frank i donot understand that explanation

please post in relevant forum.

to find the solution we need to derive the equation for line first,
find the slope first => Q (1;3) R(2;2) slope=(3-2)/(1-2)=-1
find y-intercept => Q (1;3) y=-1*x+b (ex. general equation formula y=ax+b) => 3=-1*1+b <=> b=4
Answer A satisfies, as the equation of line S is the same as equation of line segment QR
Answer B does not satisfy, as there can be skewing in line S upward and/or downward area on the xy-plane; the slope data is not enough to decide about the intersection of S and QR; these two lines can be parallel with the same angle (sharpness)

Select A.

Night reader wrote:
please post in relevant forum.


Answer B does not satisfy, as there can be skewing in line S upward and/or downward area on the xy-plane; the slope data is not enough to decide about the intersection of S and QR; these two lines can be parallel with the same angle (sharpness)

Select A.

yup posting here was mistake...my be i did it hastily so missed it

any way i still feel that B says two lines are parallel and paraller lines never intersect each other.
Could you illustrate when and how does those 2 lines intersect in the given condition

frank1 wrote:

Night reader wrote:
please post in relevant forum.


Answer B does not satisfy, as there can be skewing in line S upward and/or downward area on the xy-plane; the slope data is not enough to decide about the intersection of S and QR; these two lines can be parallel with the same angle (sharpness)

Select A.

yup posting here was mistake...my be i did it hastily so missed it

any way i still feel that B says two lines are parallel and paraller lines never intersect each other.
Could you illustrate when and how does those 2 lines intersect in the given condition

now that's it is clear that parallel lines do not intersect, we are open to the plethora of opportunities => we need to obtain at least one point for this equation line to evaluate if these lines are parallel or the same => the only position when these lines intersect is to have for them common points on the equation lines => they become one solid line then

Hi there!

Let me try to clarify things here...

(1) Take x=1 in y = -x+4 ("S equation") to note that y=3 ; that simply means that point Q is in the line segment AND in the line S, therefore (1) answers the question in the AFFIRMATIVE.

(2) Manhattan´s explanation is perfect, but I will try to put it clearer...

slope of LINE QR (defined by the distinct points Q and R) is -1 (as already shown in previous post) and that means that LINE QR and line S are parallel, that means: they are parallel and distinct or they are parallel and coincident.

Important: two lines in the plane are parallel or concurrent and they are concurrent if and only if they have exactly one point in common. (In other words, parallels may not be distinct, they may coincide if they have two distinct points in common; if so, they will have ALL points in common, for sure.)

All this understood, let me BIFURCATE statement (2) EXPLICITLY:

(2)
> Take line y = -x + c where c equals 4. In this case, as explained above, point Q is in S and now we know that line S is exactly the same as line QR, because they are parallel and have one (therefore all) point(s) in common (answering in the affirmative)

> Take line y = -x +c where c is a constant different of 4. In this case, as explained above, line S and line QR are parallel AND DISTINCT (because being parallel but when x =1 , y is NOT 3, means that line S does not pass on Q...), therefore answering in the negative.

I hope you get the point!

Regards,
Fabio.

Ok,i am having look in to this.
At the same time i found this

https://www.manhattangmat.com/forums/pos ... 10078.html

thanks

Hello, Frank1.

Please read my explanation carefully.

As far as the link you gave is concerned, there are many errors... like:

Line S and line segment QR are parallel, so they will not intersect unless line S passes through both Q and R, and thus the entire segment.

This is false. To say 2 lines intersect each other it is NECESSARY AND SUFFICIENT to have (at least) ONE point in common. My answer for sttm (1) is perfect, exactly because of that.

the word “parallel” should not be used in the case of coincident lines; thanks for calling this to our attention.

Mathematics is not a matter of opinion... by DEFINITION, parallel lines are what I explained before.

Regards,
Fabio.