Q. 11 E3.8( 8 Votes )

# If in triangle ABC, the co-ordinates of vertex A is (7, –4) and centroid of triangle is (1, 2), then the co-ordinates a mid point of BC isA. (–2, –5)B. (–2, 5)C. (2, –5)D. (5, –2)

The ΔABC with coordinates of A as (7, -4) and assuming B and C coordinates to be (x2, y2) and (x3, y3) respectively as shown

M is the midpoint of segment BC with coordinates as shown and G is the centroid

The vertices of ΔABC with their coordinates are

A = (x1, y1) = (7, -4) and

B = (x2, y2) and

C = (x3, y3)

G = (1, 2)

Centroid of a triangle is given by

G =

(1, 2) =

(1, 2) =

Equate x-coordinate and y-coordinate

= 1 and = 2

7 + x2 + x3 = 3 and – 4 + y2 + y3 = 6

x2 + x3 = -4 and y2 + y3 = 10

Divide by 2

= -2 and = 5

Thus midpoint M of BC is (-2, 5)

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