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...
Answers
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.
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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