Q. 34.7( 3 Votes )

Determine whether the point (-3, 2) lies inside or outside the triangle whose sides are given by the equations x + y – 4 = 0, 3x – 7y + 8 = 0, 4x – y – 31 = 0.

Answer :

Given:


x + y – 4 = 0, 3x – 7y + 8 = 0, 4x – y – 31 = 0 forming a triangle and point (-3, 2)


To find:


Point (-3, 2) lies inside or outside the triangle


Explanation:


Let ABC be the triangle of sides AB, BC and CA, whose equations x + y 4 = 0, 3x 7y + 8 = 0 and 4x y 31 = 0, respectively.


On solving them, we get A (7, - 3), B (2, 2) and C (9, 5) as the coordinates of the vertices.


Let P ( 3, 2) be the given point.


Diagram:



The given point P ( 3, 2) will lie inside the triangle ABC, if


(i) A and P lies on the same side of BC


(ii) B and P lies on the same side of AC


(iii) C and P lies on the same side of AB


Thus, if A and P lie on the same side of BC, then


21 + 21 + 8 – 9 – 14 + 8 > 0


50 × - 15 > 0


- 750 > 0,


Which is false


Hence, the point ( 3, 2) lies outside triangle ABC.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of lineVarious Forms of Equations of lineVarious Forms of Equations of line45 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Slope, inclination and angle between two linesSlope, inclination and angle between two linesSlope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of lineInteractive Quiz on Equations of lineInteractive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quizStraight line | Analyse your learning through quizStraight line | Analyse your learning through quiz56 mins
General Equation of a lineGeneral Equation of a lineGeneral Equation of a line43 mins
Motion in a Straight Line - 06Motion in a Straight Line - 06Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 05Motion in a Straight Line - 05Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 11Motion in a Straight Line - 11Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :