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Could someone help me with this "Linear function problem"?

The equation of two adjacent sides of a rhombus are y=2x + 4 and y = -(x/3) +4 .

If A(12,0) is one vertex and all the vertices have positive co-ordinates, find the co-ordinates of the other 3 sides.

Plz, include full working out.

Thnx...

3 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    y = 2x + 4

    y = -x/3 + 4

    2x + 4 = -x/3 + 4

    6x + 12 = -x + 12

    7x = 0

    x = 0

    y = 2(0) + 4

    y = 4

    Therefore other vertex = (0, 4)

    Distance from, (0, 4) to (12, 0) = √(4² + 12²) = √160 = 4√10

    3rd vertex on y = 2x + 4

    (h - 0)² + (k - 4)² = 160

    h² + k² = 160

    h² + (2h + 4 - 4)² = 160

    h² + 4h² = 160

    5h² = 160

    h² = 32

    h = 4√2

    k = 2(4√2) + 4 = 8√2 + 4

    Therefore third vertex = (h, k) = (4√2, 8√2 + 4)

    Fourth vertex = (12 + (4√2 - 0), 0 + (8√2 + 4- 4))

    = (12 + (4√2, 8√2)

    So all the vertexes are

    A(12, 0),

    (0, 4),

    (4√2, 8√2 + 4),

    (12 + (4√2, 8√2)

  • vect
    Lv 7
    1 decade ago

    the 2 lines intersect at (0,4)

    find the distance between the 2 points(0,4),(12,0)

    and it is sqrt160

    draw out the graph.The other 2 points are on the right side of the graph

    slope of one of the side is y=2x+b

    use (12,0) as one of the point , find the line is y=2x-24

    Use (a,b) as another vertex on this line

    b=2a-24

    160=(12-a)^2+b^2

    solve and get (12+2sqrt3,4sqrt3)

    and the other point is (2sqrt3,4+4sqrt3)

  • 1 decade ago

    hi, i'm little confused with "find the co-ordinates of the other 3 sides", are you asking the equation of the sides? or the vertices?

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