if A(4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ABC and AD is a median , then the coordinates of D are ?
Answers
Answer:
MATHS
Let A(4,2),B(6,5) and C(1,4) be the vertices of ΔABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP:PD=2:1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:QE=2:1 and CR:RF=2:1.
(iv) What do yo observe?
[Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2:1.]
(v) If A(x
1
,y
1
),B(x
2
,y
2
) and C(x
3
,y
3
) are the vertices of ΔABC, find the coordinates of the centroid of the triangle.
Answer:
since D is the mid point of BC
coordinate of B =6,5
coordinate of C=1,4
x1=6 x2=1 y1=5 y2=4
x=x1+x2/2=6+1/2=7/2
y=y1+y2/2=5+4/2=9/2
coordinate of D are (7/2,9/2)