Q52 of 66 Page 7

For the triangle ABC formed by the points A (4, -6), B (3, -2) and C (5, 2), verify that median divides the triangle into two triangles of equal area.(CBSE 2014)


⸪ AD is the median, D is the mid-point of B and C.


Co-ordinates of D = =


Area of triangle (x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2))


⸫ Area of ΔABD =


= = -3 sq. units


= 3 sq. units [⸪ Area cannot be negative]


⸫ Area of ΔADC =


= = -3 sq. units


= 3 sq. units [⸪ Area cannot be negative]


⸫ ar (ΔABD) = ar (ΔADC) = 3 sq. units


⸫ The median divides the triangle into two equal areas.

More from this chapter

All 66 →
50

The three vertices of a parallelogram ABCD are A (3, -4), B (-1, -3) and C (-6, 2). Find the coordinates of vertex D and find the area of ABCD.(CBSE 2013)

 51

If the points A (1, -2), B (2, 3), C (-3, 2) and D (-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.(CBSE 2013)

 53

Points p, Q, R and S divide the segment joining the points A (1, 2) and B (6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.(CBSE 2014)

 54

Find the ratio in which the line segment joining the points A (3,-3) and B (-2, 7) is divided by x-axis. Also, find the coordinates of the point of division.(CBSE 2014)