Perpendicular lines, and trapezoids?

alright,i have two more math questions i need a little help with :]

firstly, i have no idea how to find somethings perpendicular line, i know it is the oppopsite, but i dont know how to find it when im given a line

so, for example

how would i find the perpendicular line to: y=2x+5

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secondly, im also confused about finding the area of a trapezoid? when given each base [top and bottem] and two heights, how would i find it?

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  • 1 decade ago
    Best Answer

    The slope-intercept form of a line is y = mx + b,

    where m is the slope of the line and b is the y-intercept.

    When two lines are parallel, they will have the same slope and when they are perpendicular, their slopes will be negative reciprocals of each other. In other words, if the slope of one line is a, then the slope of the line perpendicular to it will be (-1/a).

    So, for your line, you can see that its slope is 2. (See slope-intercept form above). Therefore, the line perpendicular to it will be y = (-1/2)x + 5, and since they have they same y-intercept, that will be their point of intersection.

    The formula for finding the area of a trapezoid is

    Area = 1/2(a + b)h, where a and b are the two bases and h is the height.

    Now, your question says that you are given two heights. I find that curious because there should only be one. The height is the perpendicular distance between the two bases and since the two bases are parallel, that distance should be the same regardless of where you measure it from, so check your question again.

    Perhaps you were given the length of one or both of the slant sides of the trapezoid, in which case, you would need to use one of the trig ratios or Pythagoras' Theorem, depending on what other information you are given to find h.

    Hope this helps.

  • 1 decade ago

    there is no single perpendicular line to that equation

    anything in the form of y=-1/2 X + something will be perpendicular

    it just has to have a perpendiculat slope, which is the negative reciprocal

    with the trapezoid, as long as the two bases are the parallel ones, you add them together and divide by 2, and then multiply by the distance between the bases

    Source(s): me
  • 1 decade ago

    If two lines are perpendicular, their slopes multiply to -1.

    The slope of y = 2x + 5 is 2, so the slope of a line perpendicular to it is -1/2.

    Such a line has formula x + 2y = C, for some C.

  • Anonymous
    1 decade ago

    the perpendicular line to y=2x+5 is y= -1/2x +5 you do this because 2x is the slope, and you have to find the complete opposite of the slope of that line to get the one perpendicular to it

    sry, i dont know how to do the second one...i used to know but i forgot :)

    Source(s): me
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  • 1 decade ago

    ok so 2 is the slope so you take the negative reciporcal. meaning you flip the fraction 2/1 goes to 1/2 and then ultiply by negative one so -1/2

    well the height you need is the perpindicular height ( the height that is a straight line up and down not the slant height) then using that you add the two bases then multiply that by the height and then divide all of that by 2

  • 1 decade ago

    perpendicular lines have slopes that are negative reciprocals of each other so the perpendicular line of y=2x+5 is y=-1/2x+b where b can be any real number

    area of trapezoid is (base_1*base_2)*0.5*height

  • Anonymous
    1 decade ago

    1st-The slopes of perpendicular lines are the opposite reciprocal and can have any y intercept. so for for example, a perpendicular line of y=2x+5 is y=-1/2x+18

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    2nd-the formula for area of a trapezoid s 1/2height(sum of the bases) the height is perpendicular from one base to the other base.

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