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If 3 given points are collinear, then the area of the triangle is zero. For P(x1, y1), Q(x2, y2) and R(x3, y3), the area of the triangle is So, 1/2 X [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] = 0 For the given set of points, area of the triangle = (1/2) X [2(a - 7) + 5(7 - 3) + 6(3 - a)] = 0 Or, (1/2) X [2a - 14 + 20 + 18 - 6a] = 0 Or, (1/2) X (24 - 4a) = 12 - 2a = 0 So, 2a = 12 And a = (12/2) = 6
The speed of a boat in downstream is 20% more than speed of boat in still water. If the boat travels a distance of 90 km upstream in 15 hours then find...
A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him t...
A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and...
A man swims downstream 60 km and upstream 36 km, taking 12 hr each time. Find the man’s rate in still water?
The ratio of the speed of boat ‘A’ in still water, the speed of boat ‘B’ in still water and the speed of the current is 7:4:2, respectively. If ...
A swimmer swims from a point A against a current for 12 minutes and then swims backwards in favour of the current fornext 12 minutes and comes to the po...
A boat covers 35 km downstream in 2 h and covers the same distance upstream in 7 h. Find the speed (in km/h) of the boat in still water.
Speed of boat in downstream is 45% more than speed of boat in still water. If speed of stream is 9 km/h, then find the time taken by the boat to cover 8...
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 5 hour to row to a place and come back, how far is the place?
A boat goes 52 km in upstream in 4 hours and takes 3 hours to complete a distance of 21 km in downstream. Find the speed of boat in still water.
