Question

16. (i) If A(3, 4), B(7, - 2) and C(-2, -1) are the vertices of a AABC, write down the equation of
the median through the vertex C.
(ii) A(2, 5), B(-1, 2) and C(5, 8) are the vertices of a AABC, M is a point on AB such thai
AM: MB = 1 : 2. Find the co-ordinates of M. Hence, find the equation of the line passing
through the points C and M.​

Answer 1

Explanation:

i)

A(3,4)

B(7,-2)

C(-2,-1)

m(AB)=y2-y1/x2-x1

= -2-4/7-3

= -6/4

= -3/2

m(AB)*m(C)= -1

-3/2*m(C)= -1

m(C)= 2/3

equation

y-y1-m(x-x1)

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

3y+3=2x+4

3y-2x-1=0

ii)

A(2,5)

B(-1,2)

C(5,8)

M(x,y)=(mx2+nx1/m+n , my2+ny1/m+n)

=(1*-1+2*2/2+1 , 1*2+2*5/1+2)

=(-1+4/3 , 2+10/3)

=(3/3 , 12/3)

=(1,4)

m(MC)=y2-y1/x2-x1

=8-4/5-1

=4/4

=1

equation

y-y1-m(x-x1)

y-4=1(x-1)

y-4=x-1

y-x-3=0