Question

If a , b, and c are in Arithmetic Progression, then the straight line ax + by + c = 0 will always pass through the point:
a) (- 1, -2)
b) (1, -2)
c) (-1 , 2)
d) (1, 2)

Answer 1

Please help.

Answer 2

we should know that the slope of the line is: -a/b

Answer 3

0 = -a/b x - c

is then what we have to conform to i believe

Answer 4

I think so.

Answer 5

well, -c/b on the end i spose would be more accurate

Answer 6

when x=0, -c/b = 0 means that c=0

so:

y = -a/b x seems like a fair assumption

Answer 7

i gotta re think that :)

Answer 8

ax +by + c = 0

ax + by = -c

y = (-ax -c) /b

no zero involved .....

Answer 9

If a, b and c are in AP, then doesn't this imply:
b = a + d
c = a + 2d

where d is the difference between each term of the AP?

Answer 10

good, good

Answer 11

Then, how to proceed next?

Answer 12

if my line equation is useful; maybe sub in so that it all speaks in a?

Answer 13

Then you can rewrite your equation as:

ax + (a+d)y + a + 2d = 0

and see for which point this equation holds true?

Answer 14

\[y = \frac{-ax -(a+2d)}{a+d}\]
would be the same set up i believe

Answer 15

yes it would

Answer 16

So the exact option?

Answer 17

Aadarsh: just put each pair of values into the equations and see which one works

Answer 18

a) (- 1, -2)
b) (1, -2)
c) (-1 , 2)
d) (1, 2)

trial and error ....

\[-2 \ =^? \frac{a -(a+2d)}{a+d}\]
\[-2 \ =^? \frac{-a -(a+2d)}{a+d}\]
\[2 \ =^? \frac{a -(a+2d)}{a+d}\]
\[2 \ =^? \frac{-a -(a+2d)}{a+d}\]

Answer 19

\[2 \ =^? \frac{-a -(a+2d)}{a+d}\]
\[2 \ =^? \frac{-a -a-2d}{a+d}\]
\[2 \ =^? \frac{-2a-2d}{a+d}\]
\[2 \ =^? -2\frac{a+d}{a+d};F\]

Answer 20

-1,-2 would then seem to be appropriate to me

Answer 21

Is it? I wrote (-1, -2), just guessing.

Answer 22

amistre: I get a different result.
Aadarsh: what do you get?

Answer 23

i got a typo in my cerbral cortex; :)

1,-2 might be better; would have to test it out

Answer 24

:) - I concur

Answer 25

Yes, (1, -2) is the only correct answer.