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    Ordinary level, Co-ordinate geometry please help , really stuck !!!!! :( vicky97

    let E be the point where this perpendicular line through c intersects AB. Calculate the cordinates of E .( C =(4,-2) , A=(3,6) B=(-6,0).

    Also which is shorter distance. [CD] or [CE]? Find this distance.

    I have no clue what to do .

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      qed2923

      Find slope & eqt of AB.

      find eqt of perpendicular line through c. Use perpendicular slope slope to AB

      E = pt of intersection of the two lines.

      No pt D ???

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      Ms. L. Witter

      You found D in an earlier part of the question - I think it was the midpoint part of the question.

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      Aedamar

      Hi Vicky if you post the exact question, even a picture of it i can help you.

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      helena12140

      you use fomula?

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      Leetkd

      this is in the exam papers yes what year and question

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      Dazzla16

      Hey Vicky!

      This is what you do:

      Find the slope of AB

      The slope of AB is:

      y2 - y1

      _____ =

      x2 - x1

      (0) - (6)

      ______ =

      (-6) - 3

      -6/-9= 2/3

      That means the perpendicular slope is -3/2

      Now you have to find the equation of the line with point C (4, -2) and a slope of -3/2

      This is how:

      y - y1 = m(x - x1)

      y - (-2) = -3/2(x - (4))

      y + 2 = -3/2x + 6

      y = -3/2x + 4

      That is the equation of the line with point C and a slope of -3/2

      Now you have to find the intersection point of the lines [AB] and C to locate E.

      First, we need to find the equation of the line [AB]

      y - y1 = m(x - x1)

      y - (6) = 2/3(x - (3))

      y - 6 = 2/3x - 2

      y = 2/3x + 4

      Then use your two equations to solve simultaneous equations to find the point E

      Rearrange the two equations so that the variables (numbers with letters) are on one side, and a number on the other side

      3/2x + y = 4

      -2/3x + y = 4

      You can now solve these simultaneous equations. Just subtract the equations.

      You end up getting:

      13/6x = 0

      x = 0

      Substitute it back in to one of the equations:

      3/2(0) + y = 4

      y = 4

      The point E is located at (0,4)

      There you go!

      By the way, you never gave information about point D. But anyway, here's the distance of [CE]

      [CE] = square root((x2 - x1)^2 + (y2 - y1)^2)

      = square root((4 - 0)^2 + (-2 - 4)^2)

      = square root(4^2 + (-6)^2)

      = square root(16 + 36)

      = square root(52)

      = 2(square root(13))

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