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Finding if a point lies in a triangle

Is there a way to solve this problem without sketching a graph, using inequalities?

Reply 1
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
Is there a way to solve this problem without sketching a graph, using inequalities?



I would definitely sketch
I doubt it, at least not an efficient method so to speak. All 3 lines come together to make the triangular construct meaningful, considering each in isolation would not serve to pinpoint the placement of a given point within the subscribed area besides knowing whether the point lies above or below a particular line. Or for that matter, to the right or left of it.

Unless the equations of the lines are rendered in a less sophisticated manner, eg x=2, y=4, then mapping things out without a graph would be reasonably efficient.

Peace.
Original post by TeeEm
I would definitely sketch


For that question in the mark scheme there is just an answer so I guess you can use whatever method you want.


What about this question it explicitly states you will get less marks if you provide a graphical solution. I can do it by sketching graphs but no idea how to do it without sketching graphs.

Reply 4
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
For that question in the mark scheme there is just an answer so I guess you can use whatever method you want.


What about this question it explicitly states you will get less marks if you provide a graphical solution. I can do it by sketching graphs but no idea how to do it without sketching graphs.



I am not providing a graphical solution
I need to sketch to see the inequalities which I need to use
Original post by khanpatel321
For that question in the mark scheme there is just an answer so I guess you can use whatever method you want.


What about this question it explicitly states you will get less marks if you provide a graphical solution. I can do it by sketching graphs but no idea how to do it without sketching graphs.




one way is to find the equation of the circumcircle and see if it intersects with y = 2x + 2...
Original post by TeeEm
I am not providing a graphical solution
I need to sketch to see the inequalities which I need to use


Oh ok I see.

I get the inequalities

-2x + y < 1

3x + y < 6

2y - x >2

Sub in the three points and the only one that is true for all of the inequalities lies in the triangle. So point (1,2).


How would you use inequalities to work out the second question I posted

Original post by the bear
one way is to find the equation of the circumcircle and see if it intersects with y = 2x + 2...


He wants you to use inequalities.
Original post by khanpatel321
Oh ok I see.

I get the inequalities

-2x + y < 1

3x + y < 6

2y - x >2

Sub in the three points and the only one that is true for all of the inequalities lies in the triangle. So point (1,2).


How would you use inequalities to work out the second question I posted



He wants you to use inequalities.


:yawn:
Reply 8
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
Oh ok I see.

I get the inequalities

-2x + y < 1

3x + y < 6

2y - x >2

Sub in the three points and the only one that is true for all of the inequalities lies in the triangle. So point (1,2).


How would you use inequalities to work out the second question I posted



He wants you to use inequalities.


Am I doing your "STEP homework"?
Original post by TeeEm
Am I doing your "STEP homework"?


Just looking for help.

Like the first question you said

I am not providing a graphical solution
I need to sketch to see the inequalities which I need to use

and I used this to work out the first question using inequalities.

Just looking for a pointer so I can do the same for the second question :smile:
Reply 10
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
Just looking for help.

Like the first question you said

I am not providing a graphical solution
I need to sketch to see the inequalities which I need to use

and I used this to work out the first question using inequalities.

Just looking for a pointer so I can do the same for the second question :smile:


Have a little think
you are posting way too fast to even have looked at the problem seriously.
Have you any thoughts or ideas?
Original post by TeeEm
Have a little think
you are posting way too fast to even have looked at the problem seriously.
Have you any thoughts or ideas?


Yes you're right.

Draw a sketch

triangle is bounded by the following inequalities

x<= 1

y<= 1

x + y >= 1

y = 2x + 2 x-axis intercept y = 0 x = -1

if the line intersects the triangle then
x <=1
y <=1
x + y >=1

-1 <= 1
0<= 1
-1 is not >= 1

do the same for y - axis intercept x=0 y=2

0<=1
2 is not <= 1
2 >= 1

Line does not intersect the triangle?
(edited 8 years ago)
Reply 12
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
Yes you're right.

Draw a sketch

triangle is bounded by the following inequalities

x<= 1

y<= 1

x + y >= 1

y = 2x + 2 x-axis intercept y = 0 x = -1

if the line intersects the triangle then
x <=1
y <=1
x + y >=1

-1 <= 1
0<= 1
-1 is not >= 1

do the same for y - axis intercept x=0 y=2

0<=1
2 is not <= 1
2 >= 1

Line does not intersect the triangle?


line definitely does not intersect the triangle
Original post by TeeEm
line definitely does not intersect the triangle


Is my method correct, can't check mark scheme as there isn't one up yet.
Reply 14
Avatar for TeeEm
TeeEm
19
Original post by khanpatel321
Is my method correct, can't check mark scheme as there isn't one up yet.


if x>=1, y in the line >=4
if y<=1, x in the line <= -1/2
y=2x+4 does not intersect

Draw a picture and see what I am saying

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