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Math Help - coordinate geometry

  1. #1
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    coordinate geometry

    the line y=2x+3 intersects the y-axis at A.The points BC on this line are such that AB=BC.The line through B perpendicular to AC passes through the point D(-1,6).Calculate

    a)the eqn. of BD.
    b)coordinates of B
    c)coordinates of C

    2)given that coordinates in each of the following,find the perpendicular bisector of AB.
    a)A(1,2) B(3,4)
    b)A(2,3) B(-1,9)

    3)the line 3x+y=8 interscects the curve 3x^2+ y^2=28 at A and B.Find,
    a)the length of AB
    b)the equation of the perpendicular bisector of AB.
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  2. #2
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    Quote Originally Posted by tyana21 View Post
    the line y=2x+3 intersects the y-axis at A.The points BC on this line are such that AB=BC.The line through B perpendicular to AC passes through the point D(-1,6).Calculate

    a)the eqn. of BD.
    b)coordinates of B
    c)coordinates of C

    ...
    1. Draw a sketch of the given straight line, the point D and the perpendicular line to AC.

    2. The slope of the perpendicular line must be m=-\frac12 . Use the point-slope-formula:

    y-6=-\frac12(x+1)~\implies~\boxed{y =-\frac12 x+\frac{11}2}

    3. The point B is the point of intersection between the given line and the perpendicular line:

    -\frac12 x+\frac{11}2=2x+3~\implies~x = 1~\implies~y=5

    Therefore the point B has the coordinates B(1, 5)

    4. The point C has the coordinates C(2, 7) (You should now be able to explain how I got this result: Use the definition of slope and the equation of the given line)
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