# Vector Question

• Jun 9th 2010, 05:23 PM
Ari
Vector Question
Okay so i want to know if i have a triangle in a plane how do i know if a point is within it or not without graphing?

The question is that i have points (-1,7) and (8,-4)

i want to know if the the points (2,-1), (3,2) and (1,5) are in the triangle fromed by the origin and (-1,7) and (8,-4), outside the triangle, or on the boundary.

• Jun 9th 2010, 05:46 PM
slider142
The point must satisfy three inequalities; it must lie on the proper sides of all three lines making up the triangle.
For example, consider the line connecting (-1, 7) and (8, -4), which is (-4 - 7)/(8 + 1) = (y - 7)/(x + 1) or y = -(11/9)x + 5 + 7/9. To find the proper side for this line, test the third point (0, 0) to get the inequality y < -(11/9)x + 5 + 7/9.
Do the same for the remaining two lines.
A point is on the boundary if it satisfies the line equation, and is outside the triangle if it does not satisfy one of the inequalities and does not satisfy any equality.
• Jun 9th 2010, 06:33 PM
Ari
Quote:

Originally Posted by slider142
The point must satisfy three inequalities; it must lie on the proper sides of all three lines making up the triangle.
For example, consider the line connecting (-1, 7) and (8, -4), which is (-4 - 7)/(8 + 1) = (y - 7)/(x + 1) or y = -(11/9)x + 5 + 7/9. To find the proper side for this line, test the third point (0, 0) to get the inequality y < -(11/9)x + 5 + 7/9.
Do the same for the remaining two lines.
A point is on the boundary if it satisfies the line equation, and is outside the triangle if it does not satisfy one of the inequalities and does not satisfy any equality.

cool thanks im begginign to understand

is this equation you put right? y = -(11/9)x + 5 + 7/9