geometry q: where is line k??

[fdv]

Hi, the answer to q below is 90 degrees. i understand that lines L and W are perpendicular but why is line k perp? my answer was E as there is no info on K. What am I missing? Please advise. thanks!

Line l is defined by the equation y - 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w?
0

30

60

90

It cannot be determined from the information given.

[TP]

Hi, the answer to q below is 90 degrees. i understand that lines L and W are perpendicular but why is line k perp? my answer was E as there is no info on K. What am I missing? Please advise. thanks!

Line l is defined by the equation y - 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w?
0

30

60

90

It cannot be determined from the information given.

If k does not intersect line l it must be parallel to line l, hence perpendicular to like w.

[fdv]

thank you. i overlooked the fact that they should intersect if not parallel.

[jwinawer]

nice work tp. that's right - they buried a little trick about parallel lines into that one!

[sumit]

hi

can u pls confirm if your conclusion that line l and w are perp. is based only on the fact that the product of their slopes is -1?

Is this a firm principle, are there any more such principles to take note of in case of lines?

[esledge]

Hi Sumit,

Yes, you can conclude that lines l and w are perpendicular based solely on their respective slopes.

line l: y = 5x + 4, slope = 5.
line w: 10y = -2x - 20, so y = (-1/5)x - 2, slope = -1/5.

The product of the slopes of perpendicular lines is always -1, as is true here: (5)(-1/5) = -1.

The only other rule about slopes is that parallel lines have the same slope as each other. That rule was used in this problem, too. Line k is parallel to line l, so line k has slope = 5.