Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Banner 9
AI Mentor
Check Your IQ
Free Expert Demo
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course
Offline Centres

Q.

The line segment joining the points A(2,1)   and B(5,−8)   is trisected at the points P  and Q   such that P   is nearer to A  . Find the coordinates of P and Q.


see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.
An Intiative by Sri Chaitanya

a

P(3,2) and Q=(4,−5)  

b

P(3,−2) and Q=(4,5)  

c

P(3,2) and Q=(4,5)  

d

P(3,−2) and Q=(4,−5)   

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

It is given that
P and Q are the points of trisection of the line segment joining the points A(2,1) and B(5,-8).
We know that,
If points M and N divide the line segment XY into three equal parts, then M divides XY in the ratio of 1:2 and N divides XY in the ratio of 2:1.
Then point P divides the line AB in the ratio of 1:2 and Q divides the line AB in the ratio of 2:1.
Then,
We know that, if point O divides the line segment joining Mx1,y1 and N(x2,y2) in the ratio m1:m2, then the coordinates of O will be
m 1 x 2 + m 2 x 1 m 1 + m 2 , m 1 y 2 + m 2 y 1 m 1 + m 2  .
By using above section formula,
Coordinates of the point P is
P= 1×5+2×2 1+2 , 1×(−8)+2×1 1+2 ⇒P= 5+4 3 , −8+2 3 ⇒P= 9 3 , −6 3 ⇒P=(3,−2)   Similarly,
Coordinates of the point Q is
Q= 2×5+1×2 2+1 , 2×(−8)+1×1 2+1 ⇒Q= 10+2 3 , −16+1 3 ⇒Q= 12 3 , −15 3 ⇒Q=(4,−5)  
Therefore,
P(3,−2) and Q=(4,−5)  .
Hence, option (4) is correct.
 
Watch 3-min video & get full concept clarity
score_test_img

courses

No courses found

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Online Course for IIT JEE
Best Online Course for NEET
Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Online Course for IIT JEE
Best Online Course for NEET
Best Online Course for CBSE
whats app icon