Question

(a) The mid-point of the line segment joining
(2a, 4) and (-2,2b) is (1, 2a + 1). Find the values
of a and b.
(b) Find the equation of the line parallel to the line
3x +2y = 8 and passing through the point (0,1).
(c) If the line joining the points A (4, -5) and
B (4, 5) is divided by the point P such that
AP 2
find the co-ordinates of P. (ICSE 2007)
AB 5

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Answer 1

Answer:

Explanation:

Let AB be the line segment

A:(2a,4)

B:(-2,3b)

P(midpoint):(1,2a+1)

As P is midpoint, AP=PB

So the ratio of the segment is- AP:PB=1:1=m:n

Let

A be (x1,y1)

P be (X,Y)

B be (x2,y2)

X=1

Y=2a+1

Using section formula:

X,Y=

So now,

X=[(2a)+(-2)]/2

=>1=(2a-2)/2

=>2=2a-2

=>2a=2+2

=>2a=4

=>a=4/2

a=2

And,

Y=[(4)+(3b)]/2

=>(2a+1)=(4+3b)/2

=>(2a+1)/2=4+3b

We know the value of a, so we will put here,

=>(2(2)+1)×2=4+3b

=>(4+1)2=4+3b

=>5×2 - 4=3b

=>10–4=3b

=>6=3b

=>b=6/3

b=2

So the values of a and b are 2 and 2.

So,

A=2(2),1

=4,1

P=1,2(2)+1

=1,5

B=-2,3(2)

=-2,6

Thanks

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Answer 2

Explanation:

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