- 25. Find the co-ordinates of the centroid of ΔABC whose vertices are A(7, -3), B(5, -4) and C(-3, -5)?

A.) 3, -3 B.) 3, -4 C.) 4, -3 D.) None of these Answer: Option 'B'

x_{1}= 7, x_{2}= 5, x_{3}= -3 and y_{1}= -3, y_{2}= -4, y_{3}= -5

= [(7 + 5 - 3)/3, (-3 - 4 - 5)/3]

= (12-3)/3, -12/3)

= (9/3, -12/3)

= (3, -4) - 26. The co-ordinates of the end points of a diameter AB of a circle are A(-6, 8) and B(-10, 6). Find the

co-ordinates of its centre.

A.) -8, 7 B.) -7, 8 C.) 7, -8 D.) -8, -7 Answer: Option 'A'

The center O is the mid point of AB.

Co-ordinates of O are [(-6-10)/2, (8+6)/2]

= -16/2, 14/2

= (-8, 7) - 27. Find the co-ordinates of a point P which divides the join of A(5, -4) and B(10, 8) in the ratio 3 : 2.

A.) 9, 5 B.) 7, 8 C.) 8, 7 D.) 9, -7 Answer: Option 'C'

Required point is P = (mx_{2}+ nx_{1})/m+n, (my_{2}+ ny_{1})/m+n

P((3(10) + 2(5))/5, (3(15) + 2(-5))/5)

=(30 + 10)/5, (45-10)/5

= P(8, 7) - 28. A point C divides the join of A(2,5) and B(3,9) in the ratio 3 : 4. The co-ordinates of C are:

A.) (15/7, 46/7) B.) (15/7, 47/7) C.) (15/7, 40/7) D.) None of these Answer: Option 'B'

x_{1}=2, x_{2}=3 and y_{1}=3, y_{2}=7

= [(3*3 + 4*2)/7, (3*9 + 4*5)/7]

= 9+6/7, 27+20/7

= (15/7, 47/7) - 29. The end points of a line segment AB are A(-6, 4) and B(12,24). Its midpoint is:

A.) (14, 4) B.) (-4, 14) C.) (3, 14) D.) (-3, 14) Answer: Option 'C'

Midpoint is C((-6+12)/2, (4+24)/2)

(-6/2, 28/2) = (-3, 14)

Division of a line segment by a point :

a) If a points P(x,y) divides the join of A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m : n, then

x = (mx_{2}+ nx_{1})/m+n and y = (my_{2}+ ny_{1})/m+n

b) If A(x_{1}, y_{1}) and B(x_{2}, y_{2}) be the end points of a line segment AB, then the co-ordinates of

mid-point of AB are

(x_{1}+ x_{2})/2, (y_{1}+ y_{2})/2].

Students can learn and improve on their Cognitive and Mathematical Fast Calculation skills and prepare for competitive examinations like...

- All I.B.P.S and Public Sector Bank Competitive Exam
- Common Aptitude Test (CAT) Exams
- UPSC Paper-II or CSAT Exams
- SSC Competitive Exams
- Defence Competitive Exams
- L.I.C / G.I.C AO and Clerk Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- Career Aptitude Test (IT Companies) and etc.

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