prova de matemática ib, Exercícios de Matemática

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The movement of a robot football match have been mapped on a set of axes where (0,0) is the center of the pitch and the following equations represent the movement of the ball. Identify i the parallel movements à the perpendicular movements a y=2x+5 b y=5x+2 c y-5x=2 d y-7=2x e y-2x-6 f y+0.2x-6 g y=-2x-5 h y=2 Lo y=2x j y=5x k y=0.5x . Lo y=-0.5x m 2x=y n x-Ey a Show that a robot going in a straight line through the points (—4,3) and (11,6) will meet a robot going through the point (1,2) and (2,5) b Find the equation representing their movements c where they meet The ball is moving in the direction y = 4x+3. A robot is standing on (-1,3) a find the equation of the shortest pass to the line representing the movement of the ball. b find where the robot will catch the ball. Two robots moving in perpendicular direction met at (4,-4) if one of the robots came from (3,6), a find the equation of the second robot. b find the two possible original positions of the second robot if he travels as much as the other robot to reach (4, 4) A robot comes in the direction y + x =-3 . The goalkeeper who is standing on (—10,0) wants to send him the ball making the shortest distance. a Find the equation of the ball making shortest pass between the goal keeper and the other robot. b Find where the robot will catch the ball. The goal keeper only moves on the line x = 15 two strikers are located at Sl (13,3) and 52 (12,-2). Find the best position to stand so that the combined distance from its position to both striker is shortest.