the quadrilateral ABCD and has three verticies: A(0,0) B(3,4) C(8,4)?

how do you find the forth vertex for D, for

a) rhombus

b) isosceles trapezoid

c)kite

4 Answers

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  • 9 years ago
    Favorite Answer

    sketch the three point on graph paper.

    A is at the origin, B and C are on the line y = 4.

    A rhomus has all 4 sides equal. See first refernce below.

    So the length of the top line (going from B to C) must be the same length as the line going from the origin out to the right. The length of B C is 8 - 3 = 5 . So the point to the right of the origin must be 5 over from (0, 0) so ==> (5, 0)

    An isosceles trapezoid has a slant up a flat top and a slant down. The slant up and down are mirror images of each other (see second reference)

    So the distance directly below the point C to the end of the trapezoid must be the same as the distance directly below B to the orgin. This is 3. So D is 8 + 3 = 11 So ==> (11,0)

    For a Kite the distance from the A to B and A to D must be the same and

    The distance from C to B and C to D must be the same.

    We already have this with the rhombus. All sides have a length of 5. So D = (5,0)

    Hope this helps.

  • Ossi G
    Lv 7
    9 years ago

    Hello

    AB = √(3^2+4^2) = 5 and BC = 5

    --> AB = BC = 5

    a) slope of AC = 4/8

    slope of BD is then - 8/4

    line BD is

    y = -2x + b put in B

    4 = -2*3 + b --> b = 10

    y = -2x + 10

    find intersection point E with AC

    -2x + 10 = x/2

    10 = 5/2*x

    x = 4

    y = 2

    vector BE = E-B = (1, -2)

    double BE = (2, -4)

    add double BE to B

    D = (3, 4) + (2, -4) = (5, 0) <--- ans.

    b) add horizontal distance AB to horizontal distance of C:

    D = (11, 0)

    c) any point on the line

    y = -2x + 10

    e.g., set x = 10, --> y = - 10

    D = (10, -10) or (8, - 6)

    Regards

  • 9 years ago

    plot the points and use the properties of the objects to predict where teh last vertex is

    a rhombus has all congruent sides. in your example, the sides are 5 units long. which point is 5 units from the two other corners

  • masri
    Lv 4
    4 years ago

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