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 is

A. (–2, –5)

B. (–2, 5)

C. (2, –5)

D. (5, –2)

Answer :

The ΔABC with coordinates of A as (7, -4) and assuming B and C coordinates to be (x_{2}, y_{2}) and (x_{3}, y_{3}) 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 = (x_{1}, y_{1}) = (7, -4) and

B = (x_{2}, y_{2}) and

C = (x_{3}, y_{3})

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 + x_{2} + x_{3} = 3 and – 4 + y_{2} + y_{3} = 6

⇒ x_{2} + x_{3} = -4 and y_{2} + y_{3} = 10

Divide by 2

⇒ = -2 and = 5

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

Rate this question :

Let us write by calculating what value of K, the points (1, –1), (2, –1) and (K, –1) lie on same straight line.

West Bengal MathematicsLet us write the co-ordinates of centroid of triangle formed by the three points (x – y, y – z), (–x, –y) and (y, z).

West Bengal MathematicsThe co-ordinates of centroid of triangle is (6, 9) and two vertices are (15, 0) and (0, 10); let us find the co-ordinates of third vertex.

West Bengal MathematicsLet us prove that the line joining two points (1, 2) and (–2, –4) passes through origin.

West Bengal MathematicsThe co-ordinates of centroid of a triangle formed by the three points (7, –5), (–2, 5) and (4, 6) is

West Bengal MathematicsThe co-ordinates of mid-points of the sides of a triangle ABC are (0, 1), (1, 1) and (1, 0); let us find the co-ordinates of its centroid.

West Bengal MathematicsIf (0, 0), (4, –3) and (x, y) are collinear then

West Bengal MathematicsIf 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 is

West Bengal MathematicsLet us prove that the midpoint of line segment joining two points (2, 1) and (6, 5) lie on the line joining two points (–4, –5) and (9, 8).

West Bengal MathematicsIf the three points (a, 0), (0, b) and (1, 1) are collinear then let us show that