निम्न समीकरणों से घिरे हुए क्षेत्र का क्षेत्रफल (वर्ग इकाई में) क्या है?

2x – 3y + 6 = 0, 4x + y = 16 और y = 0?

This question was previously asked in
SSC CGL Tier 2 Quant Previous Paper 1 (Held On: 29 Jan 2022)
View all SSC CGL Papers >
  1. 14
  2. 11.5
  3. 10.5
  4. 12

Answer (Detailed Solution Below)

Option 1 : 14
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
100 Qs. 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

दिया गया है:

2x – 3y + 6 = 0

4x + y = 16

y = 0

प्रयुक्त सूत्र:

त्रिभुज का क्षेत्रफल =  ∣x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)∣ 

गणना:

2x – 3y + 6 = 0 

⇒ 2x – 3y = -6 ....(1)

4x + y = 16  ....(2)

समीकरण (2) में 3 से गुणा करने पर,

⇒ 12x + 3y = 48 ...(3)

अब,

(1) और (3) को जोड़ने पर हमें प्राप्त होता है,

⇒ (2x + 12x) = (48 – 6)

⇒ 14x = 42

⇒ x = 3

अब, x का मान समीकरण (1) में रखते हैं,

⇒ 2 × 3 – 3y = -6

⇒ 6 – 3y = -6

⇒ -3y = -1

⇒ y = (-1 – 3) = 4

इसलिए, (x1, y1) = (3, 4)

अब,

y = 0 का मान समीकरण (2) में रखने पर,

⇒ 4x + 0 = 16

⇒ 4x = 16

⇒ x = 4

इसलिए, (x2, y2) = (4, 0)

फिर से,

हम y = 0 मान को समीकरण (1) में रखते हैं,

⇒ 2x – 0 = -6

⇒ 2x = -6

⇒ x = -3

इसलिए, (x3, y3) = (-3, 0)

अब,

त्रिभुज का क्षेत्रफल =  ∣x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)∣ 

⇒ ∣3(0 – 0) + 4(0 – 4) + (-3)(4 – 0)∣ 

⇒ ∣0 + (-16) + (-12)∣ 

⇒ ∣-16 – 12∣ 

⇒ ∣-28∣ 

⇒ 14  [मापांक में ऋणात्मक चिह्न हमेशा धनात्मक लिया जाता है]

∴ अभीष्ट मान 14 है।

Latest SSC CGL Updates

Last updated on Jul 21, 2025

-> NTA has released UGC NET June 2025 Result on its official website.

->  SSC Selection Post Phase 13 Admit Card 2025 has been released at ssc.gov.in

-> The SSC CGL Notification 2025 has been announced for 14,582 vacancies of various Group B and C posts across central government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025 in multiple shifts.

-> Candidates had filled out the SSC CGL Application Form from 9 June to 5 July, 2025. Now, 20 lakh+ candidates will be writing the SSC CGL 2025 Exam on the scheduled exam date. Download SSC Calendar 2025-25!

-> In the SSC CGL 2025 Notification, vacancies for two new posts, namely, "Section Head" and "Office Superintendent" have been announced.

-> Candidates can refer to the CGL Syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline, with the age limit varying from post to post. 

-> The SSC CGL Salary structure varies by post, with entry-level posts starting at Pay Level-4 (Rs. 25,500 to 81,100/-) and going up to Pay Level-7 (Rs. 44,900 to 1,42,400/-).

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> NTA has released the UGC NET Final Answer Key 2025 June on its official website.

More Co-ordinate Geometry Questions

More Geometry Questions

Hot Links: teen patti game teen patti 51 bonus teen patti dhani teen patti sweet