Coordinate Geometry

[albinogmat]

There is a straight line that passes through two points (-r,-s)(-t, u). Is the slope negative?
(1)-t> -r
(2)u> -s
I went for A. Is that right? Please explain.

_
Albi

[Anurag@Gurome]

There is a straight line that passes through two points (-r,-s)(-t, u). Is the slope negative?
(1)-t> -r
(2)u> -s
I went for A. Is that right? Please explain.

_
Albi

Slope of a line passing through two points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1)
In this case, slope of the line = [u - (-s)]/[-t - (-r)] = (u + s)/(r - t)

Statement 1: -t > -r implies r - t > 0, but we do not know if u + s is negative or not. It may or may not be negative; NOT sufficient.

Statement 2: u > -s implies u + s > 0, but we do not know if r - t is negative or not. It may or may not be negative; NOT sufficient.

Combining (1) and (2), r - t > 0 and u + s > 0, so slope of the line should also be > 0, which means the slope will be positive; SUFFICIENT.

The correct answer should be C.

[albinogmat]

In such problems, Should I not consider the negative or positive signs (-r (negative r) or u (postive u)) as given?

[Anurag@Gurome]

In such problems, Should I not consider the negative or positive signs (-r (negative r) or u (postive u)) as given?

No, it will not be the right approach. We do not know the value of r and u.
So, no point in considering their individual signs.
Also, since the question is talking about negativity of slope, you have to consider the ratio (y2-y1)/(x2-x1).
By only considering the signs of r and u, you cannot get the idea of the sign of slope.

[dadu]

Statement 1: -t > -r implies r - t > 0, but we do not know if u + s is negative or not. It may or may not be negative; NOT sufficient.

That is very strange. u - (-s) will be positive. Otherwise the entire question becomes meaningless. Essentially we are saying that even if it is given that a line passes thru say (5-s), it can actually pass thru say (5,3).

Very surprising.