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HorseObsessed
Lv 5
HorseObsessed asked in Science & MathematicsMathematics Β· 8 years ago

Circle O has center (7,-3) and diameter AB. If the coordinates of A are (-2,4), find the coordinates of B?

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  • mathboy
    Lv 6
    8 years ago
    Favorite Answer

    Diameter AB passes through O(7, -3). In fact O is the mid point of AB. Using equation for mid point of a line : mid point of AB where A is the point (-2, 4) and B the point (x,y) is given by

    [(x - 2)/2 , (y + 4)/2] = (7, -3)

    so (x - 2)/2 = 7 and (y + 4)/2 = -3

    giving x - 2 = 14 and y + 4 = -6

    From which x = 16 and y = -10. Point B is (16, -10)

    This is easily checked by working out the gradient of the diameter. We show that gradient AO = gradient AB. This should be -7/9.

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