# Co Ordinate Geometry - Quantitative Aptitude Problems and Solutions

```Division of a line segment by a point :
a) If a points P(x,y) divides the join of A(x1, y1) and B(x2, y2) in the ratio m : n, then

x = (mx2 + nx1)/m+n  and  y = (my2 + ny1)/m+n
b) If A(x1, y1) and B(x2, y2) be the end points of a line segment AB, then the co-ordinates of
mid-point of AB are
(x1 + x2)/2, (y1 + y2)/2].```

1. 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

x1 = 7, x2 = 5, x3 = -3 and y1 = -3, y2 = -4, y3 = -5

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

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

= (9/3, -12/3)

= (3, -4)

2. 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

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)

3. 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

Required point is P = (mx2 + nx1)/m+n, (my2 + ny1)/m+n

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

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

= P(8, 7)

4. 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

x1=2, x2=3 and y1=3, y2=7

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

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

= (15/7, 47/7)

5. 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)

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

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

Quantitative Aptitude Topics

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