Question

If A,B,C are in arithmetic progression,

then the straight line

Ax +By + C =0

always passes through which the following point :
1. (1,2)
2. (1,-2)
3. (0,0)
4. (2,-1)

Plss....Also explain how the answer get...​

Answer 1

Answer:

If A, B and C are in AP, we can imply that:

⇒ B - A = C - B (Common Differences are equal)

Hence simplifying the above equation further we get:

⇒ 2B = A + C

Transposing all terms to one side we get:

⇒ A - 2B + C = 0 ...(1)

According to the question, the equation of the straight line is:

⇒ Ax + By + C = 0 ...(2)

Comparing (2) with (1) we get:

⇒ Ax = A

Therefore 'x' = 1

⇒ By = -2B

Therefore 'y' = -2

Hence the point (x,y) is (1,-2).

Hence Option (2) is the correct answer.

Answer 2

Given :-

If  A,B,C are in arithmetic progression,  then the straight lineAx +By + C =0

To Find :-

Point

Solution :-

Ax + By + c = 0 (1)

We know that

a₂ - a₁ = a₃ - a₂

d = d

Now

Here

a₁ = A

a₂ = B

a₃ = C

Now

by putting values

B - A = C - B

B + B = A + C

2B = A + C

So,

A + 2B - C = 0 (2)

Now

A + 2B - C = Ax + By + C

Ax = A

x = A/A

x = 1

Now

-2B = By

B/By = -2

y = -2

So,

Option B is correct

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