F.3 Mathematics in Action 3A Workbook 問題 (高手請進)

丫ingB×°

2008-10-07 8:38 am

Ch.3B

5. Given that the slope of the straight line passing through A(5,a) and B(2a,7) is -2,find the value of a.

6. Prove that the three points X(9,1),Y(6,4)and Z(2,8) on a rectangular coorfinate plane are collinear.

7. In the figure, S is a point on the y-axis.If the slope of the straight line passing throught S and P(6,-2)is -(5/6), find the coordinates of S.

回答 (1)

Uncle Michael

2008-10-07 9:10 am

✔ 最佳答案

5.
Slope:
(a - 7)/(5 - 2a) = -2
a - 7 = -2(5 - 2a)
a - 7 = -10 + 4a
-3a = -3
a = 1

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6.
Firstly, find the equation of the straight line XY:
(y - 1)/(x -9) = (1 - 4)/(9 - 6)
(y - 1)/(x -9) = -1
y - 1 = -x + 9
XY: x + y - 10 = 0

Put Z(2, 8) into XY:
L.S. = (2) + (8) - 10
L.S. = 0
L.S. = R.S.
Hence, Z lies on XY.

Therefore, X, Y and Z are collinear.

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7.
S is a point on the y-axis.
Let (0, b) be the coordinates of S.

Slope of PS:
(-2 - b)/(6 - 0) = -5/6
6(-2 - b) = -5(6 - 0)
-12 - 6b = -30
-6b = -18
b = 3

The coordinates of S is (0, 3).
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