Question

how to determine if points a(-5,-3),b(-1,-1)and c(11,5) are collinear

Answer 1

collinear :three or more points that lie in a straight line

Answer 2

(ab)^2 +bc^2 not equal to ca^2

Answer 3

can you explain?

Answer 4

Get the equation of the line using the first 2 points. Then substitute the last point in this equation to check if it is satisfied. If it is, then it means the 3 points are co-linear.

Answer 5

(graphical method) can be done too, plot the points on a piece of graph paper. You should be able to tell quickly if all the points fall on a straight line. If they don't, they're noncollinear.

Answer 6

how would you get the equasion of the line?

Answer 7

okay an equation to the line is defined by
\[y = mx+c\] m = gradient and c = intercept...do u know that?

Answer 8

i know y=mx+b
where m is the slope and b is the y intercept

Answer 9

also the slope is 1/2

Answer 10

collinear means that that the slope of two adjacent points will be equal....

Answer 11

so if the slope is the same for the 3 points it is collinear?

Answer 12

yes...

Answer 13

okay so first to get the equation to a line
u need to find the "m" which is the slope/gradient
so u have two points are a(-5,-3),b(-1,-1)
\[m=\frac{{y_{2}-y_{1}}}{x_{2}-x_{1}}\]
get the values and substitute to get the M= rather the slope

Answer 14

since slope is same-they all will lie in a same straight line...

Answer 15

but what if the y intcept is different? it isnt collinear then is it?

Answer 16

@Sarkar what is theres another line parellel to that line.?

Answer 17

if*

Answer 18

so???

Answer 19

isnt there a way to determine it accurately?

Answer 20

they are not collinear, assume that theres an equation y=2x+3
and another one y=2x-3
they have differnt y values ( which further proves that the points dont lie on the same line)

Answer 21

Check if slope(ab) = slope(ac).

Answer 22

i don agree

Answer 23

the slopes are equal
m=1/2

Answer 24

You're thining a bit wrong thush

Answer 25

i agree @Ishaan94

Answer 26

slope is the gradient right?

Answer 27

rise over run is the slope

Answer 28

Then they are collinear

Answer 29

Yes, slope is gradient.

Answer 30

you are confusing it@thush,you have are considering two lines,why????
the points in Q satisfy only ONE equation not 2..

Answer 31

i thik the equasion is y=-x+2
where the 2 is the y intercept

Answer 32

what do u say now?