Q29 of 47 Page 1

If A (4, 2), B (7, 6) and C (1, 4) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.


⸪ 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 =


= = 4.5 sq. units


⸫ Area of ΔADC =


= = 4.5 sq. units


⸫ ar (ΔABD) = ar (ΔADC) = 3 sq. units


⸫ The median divides the triangle into two equal areas.


More from this chapter

All 47 →
20

Find a point P on the y-axis which is equidistant from the points A (4, 8) and B (-6, 6). Also, find the distance AP.

 27

Solve for x:

28

Five cards – the ten, jack, queen, king and ace of diamonds, are well shuffled with their faces downwards. One card is then picked up at random.

(a) What is the probability that the drawn card is the queen?


(b) If the queen is drawn and put aside, and a second card is drawn, find the probability that the second card is (i) an ace (ii) a queen.

 30

In figure 4, a triangle ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.