# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 25

This question is from Co-ordinate Geometry. Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's - you get Co-ordinate Geometry. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope. CAT exam does test one on ideas from Coordinate Geometry once in a while. It is important to cover ideas from Coordinate Geometry in your CAT Preparation.

Question 25 : The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

1. 15
2. 13
3. 14
4. 12

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

The line x + 9y + c = 0, forms one of the diagonal of the parallelogram.
The other diagonal connects the points (2, 1) and (-3, -4).

The diagonals of a parellogram bisect each other, hence the line x + 9y + c = 0 should pass hrough the midpoint of the line joining (2, 1) and (-3, -4).

The midpoint of the line joining (2, 1) and (-3, -4) = ( $$frac{2-3}{2}$ , $\frac{1-4}{2}$ ) =$ $$frac{-1}{2}$ , $\frac{-3}{2}$ ) =$-0.5 , -1.5)
Therefore, the line x + 9y + c = 0 passes through (-0.5 , -1.5),
Hence, (-0.5) + 9(-1.5) + c = 0
(-0.5) + 27(-0.5) + c = 0
28 (-0.5) + c = 0
-14 + c = 0
c = 14.

The question is "The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is"

##### Hence, the answer is, "14"

###### CAT Coaching in ChennaiCAT 2023

Classroom Batches Starting Now! @Gopalapuram

###### Best CAT Coaching in Chennai Introductory offer of 5000/-

Attend a Demo Class

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com