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Math Help - Introduction to analytic geometry?

  1. #1
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    Introduction to analytic geometry?

    Can anyone assist me in these 2 questions

    1. Find all values of a so that the distance between points (A,-9) and (-2A,7) is 20 units. I did this

    Square root (7-(-9))^2+(-2a-a)^2

    I get square root 256+9A=20 But how would I proceed taking the square root and the squaring 20?


    My next question I am not sure how to start

    Collinear points lie on the same line. Find the value of K for which the points (15,1)
    (-3,8) and (3,k) are collinear.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by homeylova223 View Post
    Can anyone assist me in these 2 questions

    1. Find all values of a so that the distance between points (A,-9) and (-2A,7) is 20 units. I did this

    Square root (7-(-9))^2+(-2a-a)^2

    I get square root 256+9A=20 But how would I proceed taking the square root and the squaring 20?
    Which variable are you solving for? A or a? Math is case sensitive!

    20 = \sqrt{(7 - (-9))^2 + (-2a - a)^2}

    20 = \sqrt{256 + 9a^2}

    Now square both sides and solve the quadratic.

    Some advice...Write out the whole line each time, not just part of it. You'll see what you need to do more easily.

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by homeylova223 View Post
    Collinear points lie on the same line. Find the value of K for which the points (15,1)
    (-3,8) and (3,k) are collinear.
    Recall the equation for a line: y = mx + b

    Three points are colinear if they fall on the same line. So you have three equations:
    1 = 15m + b
    8 = -3m + b
    k = 3m + b

    Three equations, three unknowns. (Hint: solve the first two equations for m and b first.)

    -Dan
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  4. #4
    Super Member bigwave's Avatar
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    Quote Originally Posted by homeylova223 View Post
    Collinear points lie on the same line. Find the value of K for which the points (15,1)
    (-3,8) and (3,k) are collinear.
    first find the slope m from the first 2 given points then use y-y_1=m(x-x_1) from this you should be able to see how to get k

    from this i got y=\frac{7}{18 }x +\frac{41}{6 }

    now if you plug in 3 for x then y will give the k value
    Last edited by bigwave; May 3rd 2011 at 03:39 PM. Reason: latex error
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