Question

Please answer these MCQ'S
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Answer 1

Let ABC is a triangle in which coordinates of A(x1,y1) , B(x2,y2) and C(x3,y3) .

Coordinates of mid point of AB is P(1,2) , mid point of BC is Q(0,-1) and mid

point of CA is R(2,-1) ,acordingly:-

(x1+x2)/2= 1 or. x1+x2=2…………(1) and (y1+y2)/2=2. or y1+y2=4……………(2)

(x2+x3)/2=0. or. x2+x3=0…………(3). and. (y2+y3)/2=-1. or. y2+y3=-2………(4)

(x3+x1)/2=2. or. x3+x1= 4………….(5). and. (y3+y1)/2=-1. or. y3+y1=-2………..(6)

Adding eqn. (1), (3) and (5)

2(x1+x2+x3)= 6

or. x1+x2+x3=3………………(7)

Subtracting eqn. (1) ,(3) and (5) from eqn. (7)

x3=1 , x1=3 and x2=-1.

Similarly 2(y1+y2+y3)=0. or. y1+y2+y3=0 and y3=-4. , y1=2 and y2= 2 .

Thus , A(3,2) , B(-1 , 2). and C(1,-4). Answer.

_________________________

Equation of the line joining (-1, 2) and (3, -4):

(y + 4) / (x - 3) = (2 + 4) / (-1 - 3) = (-3 / 2)

2y + 8 = -3x + 9

3x + 2y = 1……………..(1)

Equation of the other line:

2x - 3y = -4…………………(2)

Point of intersection between lines (1) and (2) must be {(-5 / 13), (14 / 13)}. Clearly, this point lies in between (-1, 2) and (3, -4). Suppose, the point splits the line in m : n ratio.

3*m + (-1)*n = (-5 / 13)*(m + n)

39m - 13n = -5m - 5n

44m = 8n

m : n = 2 : 11.

So, the ratio will be (2 : 11).

Hope it helps