Q. 155.0( 3 Votes )

Prove that the lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.

Answer :

Given: 2x – 3y + 1 = 0,


x + y = 3,


2x – 3y = 2


x + y = 4 are given equation


To prove:


The lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.


Explanation:


The given lines can be written as


… (1)


… (2)


… (3)


… (4)


The slope of lines (1) and (3) is and that of lines (2) and (4) is 1.


Thus, lines (1) and (3), and (2) and (4) are two pair of parallel lines.


If both pair of opposite sides are parallel then, we can say that it is a parallelogram.


Hence proved, the given lines form a parallelogram.


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
Straight line | Analyse your learning through quizStraight line | Analyse your learning through quizStraight line | Analyse your learning through quiz56 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
General Equation of a lineGeneral Equation of a lineGeneral Equation of a line43 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 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 - 02Motion in a Straight Line - 02Motion in a Straight Line - 0261 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 :