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Question:
The lines AB and CD are parallel to each other. Find the value of a in each of the cases.
(a) A (2, 3), B (4, 5) and C (4, 3), D (2, a)
(b) A (1, 2), B (3, 4) and C (-3, -2), D (a, 6)
(c) A (-1, -2), B (-5, -4) and C (1, 7), D (3, a)
(d) A (1, 1), B (a, 3) and C (-1, 4), D (2, 7)
^ Those are some of the questions I need help on.

Could you please give the fomulae and the explain the working out too?

2007-12-06 17:34:25 · 3 answers · asked by Anonymous in Science & Mathematics Mathematics

3 answers

Well, Say you have a line passing through two points A=(x1,y1) and B=(x2,y2), then two lines are parallel if their slopes are equal.
Slope m = (y2 - y1)/(x2 - x1)
Also, an equation for a line passing through a point A is
y-y1=m(x-x1)

Hence for
a) m = (5 - 3) / (4 - 2) = 2/2 = 1
and, y-3 = 1*(x-4) or equivalently:
y = x-1
Now, for point D=(2,a) you know x, but not why, plug into equation: y = 2-1=1, Hence D=(2,1).
Same for the others.
Hope that helps.

2007-12-06 17:46:42 · answer #1 · answered by Anonymous · 0 0

There is no special formula required. You just need to know the fundamentals of what's going on.
You have two parallel lines, so their slopes must be the same. So for any two points on a line:
(y2-y1 )/(x2-x1) = slope. Once you have the slope from one pair of points, you can work with the set of points with the unknown x or y value with the slope and the other coordiantes to solve. For example in (d), considering C-D. the slope is
(7-4)/(2- -1)= 1
Then 1= (3-1)/(a-1) and a=3.

2007-12-07 01:51:29 · answer #2 · answered by cattbarf 7 · 0 0

The easiest way is, y=mx+c (the equation of a straight line), where y is the vertical, x, the horizontal, m the gradient and c the intersection. As AB and CD are parallel,( i.e. m is equal) their respective gradients are equal. I won't give you the answer but hope that helps.

2007-12-07 02:05:39 · answer #3 · answered by Anonymous · 0 0

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