Q27 of 49 Page 1

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.


Area of triangle with vertices A (x1, y1), B (x2, y2), C (x3, y3) is given by,


(x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2))


Area (ΔABD) =


= = 12 sq. units


Now, with AB as the base and h as the height of the ΔABD,


Area (ΔABD) =


Distance between two points is given by,


=


AB =


Area (ΔABD) =


⇒ 12 =


⇒ h =


⸫ h = units


More from this chapter

All 49 →
25

In Fig. 5, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.

Prove that:


(i) AB + CQ = AC + BQ


(ii) Area (Δ ABC) = 1/2 (Perimeter of ΔABC) × r


 26

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.

 28

Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minutes. Find the rate of flow of water in the pipe in km/h.

 29

While boarding an aero plane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed/hour of the plane. Do you appreciate the values shown by the pilot, namely, promptness in providing help to the injured and his efforts to reach in time?