1 The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of triangle ABC (1)The median from A meets BC at - Maths - Coordinate Geometry

Question

1 The points
A(x1,y1),B(x2,y2) and
C(x3,y3) are the vertices of triangle ABC
(1)The median from A meets BC at D What are thEcoordinates of
the point D?
(2)Find the coordinates of the point P on AD such that AP : PD =
2:1
(3)Find the coordinates of points Q and R on medians BE and
CFrespectivelysuch that BQ : QE = 2:1 Aand CR : RF = 2 :1
(4)What are the coordinates of the centroid of the triangle
ABC?

Gursheen kaur. · Accepted Answer

SOLUTION : 
What are the coordinates of the centroid of the
triangle ABC?

Given: 
The points A(x1,y1),B(x2,y2)
and C(x3,y3)
are the vertices of triangle ABC

As we know that the centroid of a triangle is the point of
concurrency of the medians

The centroid G of the triangle ABC, divides the median AD, in the
ratio of 2 : 1

AG/AD = 2/1

Since,

D is the midpoint of BC

âˆ´Coordinates of D are
(x2+x3/2, y2+y3/2)

Using the section formula,

The coordinates of G are

â‡’(2(x2+x3/2)+1
x1/2+1, 2(y2+y3/2)+1
y1/2+1)

â‡’ Coordinates of G are [(x1+x2+x3)/3,
(y1+y2+y3)/3]