maths(28) - square

[匿名]

2011-11-13 8:16 am

1)
A(7,2) and C(1,4) are two vertices of a square ABCD.
a) Find the equation of the diagonal BD
b) Find the coordinates of B and D

(p.s. solve the problem by calculation, not graphing)

回答 (1)

用戶2053

2011-11-13 7:33 pm

✔ 最佳答案

a)The slope of AC * The slope of BD = - 1 since AC 丄 BD.(2 - 4) / (7 - 1) * The slope of BD = - 1The slope of BD = 3The mid point of AC and BD = ( (7+1)/2 , (2+4)/2 ) i.e. (4 , 3)The equation of the diagonal BD is(y - 3) / (x - 4) = 33x - y - 9 = 0
b)Let M be the centre of the square , by a) , M is (4 , 3).Let B or D be (x , y) , by a) , y = 3x - 9Since BM = DM = AM ,√ ( (x - 4)² + (y - 3)² ) = √ ( (7 - 4)² + (2 - 3)² )(x - 4)² + (3x-9 - 3)² = (7 - 4)² + (2 - 3)²x² - 8x + 16 + 9x² - 72x + 144 = 10x² - 8x + 15 = 0(x - 3) (x - 5) = 0x = 3 or x = 5
y = 0 or y = 6So B is (3 , 0) and D is (5 , 6)
or B is (5 , 6) and D is (3 , 0).

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