I could swear I've posted this one already but can't find it anywhere so here goes:
In the XY coordinate plane, Line L and Line K intersect at point (4,3). Is the products of their slopes negative?
1. The product of the x-intercepts of lines L and K is positive
2. The product of the y-intercepts of lines L and K is negative.
Please explain the rules too! thx
whoah! where did you get this problem Jen?
Well it took me some time but my answer is B. this is why:
we are give 1 point (4,3)
talks about x intercept so we have another point for L and K
L(X1, 0) and K(X2, 0)
slope L = m1 = -3/(x1- 4) --> using slope, m = (y2 - y1)/(x2 - x1)
slope K = m2 = -3/(x2-4)
m1.m2 = -9/(x1-4)(x2-4) ....can be -ve if both x1 and x2>4 or both <4. since the stmt says that x1.x2>0 it doesnt help
here we are given points L(0,y1) and K(0,y2)
slope L = m1 = (y1-3)/4
slope K = m2 = (y2-3)/4
m1.m2 = (y1-3)(y2-3)/16. this can be negative is either y1 or y2 <3
since we are given that y1.y2<0, we know that one of them is negative and one positve. therefore m1.m2 <0
Answer is B