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L: 2x + y - 6 = 0

(a) Let the coordinates of A be (a,0)
and the coordinates of B be (0,b)

Substitute the A into L
2a + 0 - 6 = 0
2a = 6
a = 3

Substitute the B into L
2(0) + b - 6 = 0
b = 6

Therefore, the coordinates of A and B are (3,0) and (0,6) respectively.

(b) Let the coordinates of the mid-point be (m,n)

m = (3+0)/2 = 3/2

n = (0+6)/2 = 3

Therefore, the coordinates of the mid-point are (3/2,3)

2x + y - 6 = 0
A = (a, 0)
B = (0, b)

When the line meet the x-axis, y=0 and x = a, so re-write the line formula:
2 (a) + 0 - 6 = 0
2 (a) = 6
a = 3
Therefore point A = (3, 0)

When the line meet the y-axis, y = b, x = 0, so re-write the line formula:
2 (0) + b - 6 = 0
0 + b = 6
b = 6
Thyerefore point B = (0, 6)

Mid-point of the line AB:

X =(x2-x1)/2 ; Y = (y2-y1)/2
X = 3/2; Y = 6/2 = 3
Therefore the midpoint AB = (3/2, 3)

Hope this helps.

X=0
2X+Y-6=0

Y-6=0
Y=6

Y=0
2X+Y-6=0
2X-6=0
X=3

(a) A point (3,0) B point (0,6)
(b) 忘記了公式......= = 給我公式計給你好嗎...