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Math Help - Slope...

  1. #1
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    Slope...

    Can you guys show me how to do these problms?? I was sick yesterday and today and wasnt able to go to my Math class...

    1.Find the eqn of the line passing thru the midpoint of the line segment joining A(-3,2)) and (1,6) with slope half the slope of the line passsing A and B

    2.Find the eqn of the line perp. to line -2x-y=-10 and having the midpot. of the segment of the line 2x+y=4 from its x-int. to its. y-int.

    3.Pts. A(-8,-16) B(0,10) and C(12,14) are three vertices of a parralelogram. Find the coordinates of the 4th Vertex if its located in the 3rd Quadrant

    4.Givenn the line 2x-3y=2, rewrte:
    a. in point slope fom
    b. in slope-int. form
    c. in 2pt. form

    Thank you guys!!!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AndrewK View Post
    1.Find the eqn of the line passing thru the midpoint of the line segment joining A(-3,2)) and (1,6) with slope half the slope of the line passsing A and B
    I presume point B is (1, 6)?

    The midpoint of the line segment between points A and B is:
    ((-3 + 1)/2, (2 + 6)/2) = (-1, 4)

    The slope of the line segement between points A and B is:
    (2 - 6)/(-3 - 1) = -4/-4 = 1

    So half of this slope is 1/2. We need the equation for the line that has a slope of 1/2 and passes through the point (-1, 4).

    y = (1/2)x + b
    where b is the y-intercept.

    To find b, just plug in a point on the line. The only point we know is (-1, 4), so...
    4 = (1/2)*(-1) + b

    4 = -1/2 + b

    b = 4 + 1/2 = 9/2

    Thus the line is:
    y = (1/2)x + (9/2)

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AndrewK View Post
    2.Find the eqn of the line perp. to line -2x-y=-10 and having the midpot. of the segment of the line 2x+y=4 from its x-int. to its. y-int.
    Let's find that midpoint first.
    2x + y = 4

    y = -2x + 4

    The y-intercept is the point (0, 4), which you can read off from the equation, or just plug in the x value of 0 and find out what y is.

    To find the x-intercept put y = 0 and solve for x:
    0 = -2x + 4

    -2x = -4

    x = -4/-2 = 2

    So the x-intercept is the point (2, 0). We need the midpoint of the line segement going from (2, 0) to (0, 4):
    ((2 + 0)/2, (0 + 4)/2) = (1, 2)

    Now we need to know the slope of the line we want. This is perpendicular to the line -2x-y=-10. Putting this into slope-intercept form:
    -y = 2x - 10

    y = (-2)x + 10

    The slope of this line is -2. Thus the slope of the line perpendicular to it is -1/(-2) = 1/2.

    So we need a line with a slope of 1/2 going through the point (1, 2). This is done in exactly the same way I showed you in the first problem. I'll give you the solution:
    y = (1/2)x + (3/2)

    If you have a problem finding this, just let me know.

    -Dan
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