F.4 MATHS

(a)
The line x = 4 is a vertical line.

Since the required line is parallel to x = 4, then the required line is also avertical line.

The x-coordinates of all points on a vertical line are equal. Since (3, -2)lies on the required line which is vertical, the x-coordinates of all points onthe required line are equal to 3.

Therefore, the equation of the required line is : x = 3


(b)
The line x = -2 is a vertical line.

Since the required line is parallel to x = -2, then the required line is a horizontalline.

The y-coordinates of all points on a horizontal line are equal. Since (3, -2)lies on the required line which is horizontal, the y-coordinates of all pointson the required line are equal to =-2.

Therefore, the equation of the required line is : y = -2

2014-09-19 11:43:37 補充：
Alternative method :

(a)
(4, -2) lies on the line x = 4
slope of the given line (x = 4) = (y + 2)/(4 - 4)

The required line // the line x = 4
slope of the required line = (y + 2)/(4 - 4)
(y + 2)/(x - 3) = (y + 2)/(4 - 4)
(y + 2)/(x - 3) = (y + 2)/0
Hence, x - 3 = 0 ...... (ans)

2014-09-19 11:43:50 補充：
(b)
The line x = -2 is a vertical line.

Since the required line is parallel to x = -2, then the required line is a horizontal line.
Slope of the required line (a horizontal) = 0

(y + 2)/(x - 3) = 0
y + 2 = 0 ...... (ans)

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http://i.imgur.com/nsGsCRE.png

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2014-09-19 11:34:45 補充：
你或者想大家解釋得詳細一點令你明白發生什麼事。

(a)
x = 4 這條線是一條 vertical line (slope 是 undefined 的)，故此不能計 slope。要明白與此線平行的線也要是 vertical line，即是屬於 x = h 的類型。
由於 x = h 會通過題目要求的 (3, -2)，所以 h = 3，而所求的線是 x = 3。

2014-09-19 11:34:54 補充：
(b)
x = -2 這條線是一條 vertical line (slope 是 undefined 的)，與此線垂直的線必定是 horizontal line (水平線)，即是屬於 y = k 的類型。
由於 y = k 會通過題目要求的 (3, -2)，所以 k = -2，而所求的線是 y = -2。

a) x=3

b) y=-2