Are the points (1,2) (3,8) and (38,113) colinear?

Question

I dont understand at all? All I know is that three points are called colinear if they lie on the same line. My hint was, use slope

Answer 1

Here's the equation for the line
y = 3X -1

Plug in coordinates to check.
1, 2 check
3, 8 check
38, 113 check

Yep, they're colinear!

Easiest way to tell is the first figure out the equation for the line connecting two point. Then, just plug in the coordinates of the third point and see if it works out.

If it does, then it's colinear. If it doesn't, it's not!

Hope that helps!

Answer 2

Let's find the equation of the line through the first 2 points.
I'll put it in the form y = mx + b.
The slope is (8-2)/(3-1) = 3
y = 3x + b.
Plugging in the point (1,2) gives 2 = 3 + b
b = -1, y = 3x - 1.
Now, plugging in the 3rd point we see
that 113 = 3*38 - 1, so all the points are collinear.
BTW, just because the slopes of the line through
points 1 and 2 and 2 and 3 are the same, does
NOT guarantee that the 3 points are collinear.
They may lie on parallel lines.

Answer 3

Let: A(1,2); B(3,8); C(38,113)

gradient of AB:
(8-2)/(3-1)=6/2=3

gradient of BC:
(113-8)/(38-3)=105/35=3

gradient of AC:
(113-2)/(38-1)=111/37=3

Since gradient of AB=gradient of BC=gradient of AC,
therefore the points (1,2) (3,8) and (38,113) are colinear

Answer 4

if points A(1,2) and B(3,8) have the same gradient as B(3,8) and C(38,113) then yes they are colinear

AB(8-2) / (3-1)= 6/2 = 3

BC(113-8) / (38-3)= 105/ 35 = 3

AC(113-2)/(38-1)=111/37=3

then yes they are colinear.

Answer 5

slope is not always correct. the slope will be same even if the lines are parallel.. you can get the answer by equating the sum of two sides with the third side in the distance formula or use section formula . another way is to put the coordinates in the area of triangle equation. if the area of triangle is zero then the points are collinear. but the easiest method would be to plot the coordinates on a graph and find out whether the points lie on the same line or not.

Answer 6

yes the points are colinear.. the condition is that they should lie on same line...... now let us find the equation of line between two points (y-y2)/(x-x2)=(y2-y1)/(x2-x1)
thus substutuing points(1,2)&(3,8) we get the equation of line as
3x-y=1.......... now if the third point has to be colinear then it has to satisfy the equation.......
thus sub (38,114)in eqation ie 3*38-113 we get 1.. thus the points are colinear

Answer 7

Determine the equation of the line passing between any two of them. Then determine the equation of the line passing between another pair. If the equations are the same, then they are colinear.

Answer 8

Your book will tell you