moneyman wrote:In the xy co-ordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative ?
(1) The product of the x intercepts of lines l and k is positive.
(2)The prodcut of the y intercepts of lines l and k is negative.
Ans C
These are the different types of slopes. For the product of the slopes of these lines to be negative either one of them has to have a negative slope and the other one has to have a positive slope.
The only information that we have of the question stem is that both the lines intersect at (4,3)
Now, the x intercept of the line is the value of x when y is 0 in the equation y=mx+c, so the x intercept of the line is x=-c/m (m is the slope). Y intercept of the line is the intercept of the line when x is 0 in the equation y=mx+c, so the y intercept of a line is y=c.
Let the eqyation of line l be y1=m1*x1+c1 and that of line k be y2=m2*x2+c2. We need to find if the product of m1*m2 is negative
The first statement says the x intercept of the 2 lines is positive. That means it says (-c1/m1)*(-c2/m2) is positive. Since we dont know what the signs ofc1,c2,m1,m2 is we cannot say if m1*m2 is negative. So this statement is insufficient.
The second statement says that the product of the y intercepts of the 2 lines is negative. That means c1*c2 is negative. But this again does not give us any idea about the sign of m1 and m2. So this statement is also insufficient.
Combine the 2 statements and we have (c1/m1)*(c2/m2) is positive and c1*c2 is negative. Now for (c1/m1)*(c2/m2) to be positive when c1*c2 is negative, m1*m2 has to be negative only then will the negative sign of the numerator of the fraction (c1/m1)*(c2/m2) cut out the negative sign of the denominator thereby keeping the fraction (c1/m1)*(c2/m2) positive. So as we can see when we combine the 2 statements we do get a definite answer that m1*m2 is negative so the answer is C.
