F.5 Maths!!!

2008-09-15 8:18 am

Please answer the following questions and please don't use some stupid methods to do them. Thanks a lot!

There are three straight lines L1, L2 and L3. L1 is perpendicular to L2 and L2//L3. L1 and L2 intersect at a point P on the x-axis. The y-intercepts of L2 and L3 are -4 and 0 respectively, and the slope of L1 is -2. Find

(a) the equation of L1, L2 and L3,
(b) the coordinates of the intersection Q of L1 and L3.

回答 (1)

Uncle Michael

2008-09-15 10:11 am

✔ 最佳答案

(a)
The slope of L1 = -2
L1 is perpendicular to L2. Hence, the slope of L2 = 1/2
The y-intercept of L2 is -4.
The slope-intercept form of L2: y = (1/2)x + (-4)
L2: x - 2y - 8 = 0

The slope of L2 = 1/2
L2 // L3. Hence, the slope of L3 = 1/2
The y-intercept of L3 is 0.
The slope-intercept form of L3: y = (1/2)x + 0
L3: x - 2y = 0

L2: x - 2y - 8 = 0
L2 cuts the x-axis at point P:
The x-axis: y = 0
Put y = 0 into L2: x - 2(0) - 8 = 0
x = 8
Hence, P (8, 0) lies on L1.
The slope of L1 = -2
The point -slope form of L1: y - 0 = -2(x - 8)
L1: 2x + y - 16 = 0

=====
(b)
L1: 2x + y - 16 = 0 ...... (1)
L3: x - 2y = 0 ...... (2)

(1):
2x + y = 16
4x + 2y = 32 ...... (3)

(2) + (3):
5x = 32
x = 6.4

Put x = 6.4 into (2):
6.4 - 2y = 0
y = 3.2

Hence, Q is (6.4, 3.2).
=

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