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an isosceles triangle on the coordinate plane has side lengths of 8,5,and 5 units. The long side is along the x-acis, find the coordinates of each vertex.

  • geometry -

    place the long side on the x-axis so that it runs from
    (0,0) to (8,0)
    then the altitude cuts the base in half and hits it at (4,0)
    looks like we have 2 right-angled triangles with base of 4 and hypotenuse of 5,
    by Pythagoras that height has to be 3
    (s^2 + 4^2 = 5^2)

    so the third vertex must be (4,3)

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