MAth 一問

6.(a)
The point-slope form of the line L:

y - 3 = (-2/3)(x - 1)

3(y - 3) = (-2)(x - 1)

3y - 9 = -2x + 2

2x + 3y - 11 = 0

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6.(b)
At the y-intercept, x = 0

Put x = 0 into the equation of L:

2(0) + 3y - 11 = 0

y = 11/3

The y-intercept is (0, 11/3)

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6.(c)
Distance between A and the point where L cuts the y-axis

Distance between (1, 3) and (0, 11/3)

= √[(1 - 0)2 + (3 - 11/3)2]

= √[12 + (-2/3)2]

= √[1 + 4/9]

= √(13/9)

= (√13)/9
=