Pkit wrote:

157. If line L passes through point (m, n) and

(– m, – n), where m and n are not 0, which of the following must be true?

I. The slope of L is positive

II. The slope of L is negative

III. L exactly passes through 2 quadrants

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only

Equation of the line with slope m passing through point \((x_1,y_1)\) \(&\) \((x_2,y_2)\)

\((y-y_1)=m(x-x_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

We have the line that is passing through \((m,n)\) \(&\) \((-m,-n)\)

\(Slope=\frac{-n-n}{-m-m}=\frac{n}{m}\)

Equation of the line will be:

\(y-n=\frac{n}{m}(x-m)\)

\(y-n=\frac{n}{m}x-n\)

\(y=\frac{n}{m}x\)

Thus we know that this line passes through the origin as the y-intercept is 0. This makes III true.

If we put, n=1 and m=1

\(y=x\); this line has a positive slope. We can count II out.

Put n=-1 and m=1

\(y=-x\); this line has negative slope. We can count I out.

Ans: "C"

_________________

~fluke

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