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12.6 Distance from a Point to Line 点到直线的距离

(1)
Find the distance from the point (2, 3) to the line 7x – 24y + 8 = 0 and prove that the point(2, 3) and the origin are at the different side of the line.

2
(2)
If P(h, k) is collinear with ( –2, 1), (1, 2), and the distance from P to the line 3x – 4y + 5 = 0 is 3 units, find the coordinate of P.

(10, 5), (-8, -1)
(3)
Find the equation of a straight line L, which is parallel to the line x + 2y –3 = 0 and the distance between them is 2 units.

x + 2y – 3 2 = 0
(4)
Two parallel lines L : 2x + 2y – 1 = 0 and L : 2x + 2y – 13 = 0.

(a) Find the y-intercept of L .

(b) Find the distance between L and L .

(c) L is another line parallel to L . If the distance between L and L is equal to that between L and L , find the equation of L .
L 为L 的另一平行线. 若L 与L 的距离和L 与L 的距离相等, 求L 之方程式.

(a) (b) 3 (c) 2x + 2y + 11 = 0

(5)
Find the equation of line which parallel with : 2x – 6y + 1 = 0 and : x – 3y – 1 = 0, and separate and (a) internally to (內分) 1 : 2,

(b) externally to (外分) 1 : 3

(a) x – 3y = 0

(b) 4x – 12y + 5 = 0

(6)
Given that the lines x + y + 3 = 0, x + 3y +7 = 0 and 2x + 3y + 5 = 0 form a triangle; find the heights of the triangle. , , (7)
ABCD is a trapezium where AB parallel to DC with the coordinates A(0,5), B(4,17), C(7, t), D(0, 0). Calculate the value of t and the distance of the two parallel lines.

ABCD为一梯形且AB与DC平行而座标A(0, 5), B(4, 17), C(7, t), D(0, 0). 求t之值及两平行线的距离.

21 , 