A translation maps a point (1,2) onto (-1,2). What would be the coordinates of the object whose image is (-3,-3) under the same translation?

Haya hapa masuluhisho ya maswali uliyotoa: A translation maps a point (1,2) onto (-1,2). What would be the coordinates of the object whose image is (-3,-3) under the same translation? Step 1: Determine the translation vector. Let the translation vector be T = a \\ b . A point (x,y) is translated to its image (x',y') by the rule: x' \\ y' = x \\ y + a \\ b Given that the point (1,2) is mapped onto (-1,2): -1 \\ 2 = 1 \\ 2 + a \\ b From the x-coordinates: -1 = 1 + a a = -1 - 1 = -2. From the y-coordinates: 2 = 2 + b b = 2 - 2 = 0. So, the translation vector is T = -2 \\ 0 . Step 2: Find the coordinates of the object. Let the object's coordinates be (x_o, y_o). Its image is given as (-3,-3). Using the same translation vector: -3 \\ -3 = x_o \\ y_o + -2 \\ 0 From the x-coordinates: -3 = x_o - 2 x_o = -3 + 2 = -1. From the y-coordinates: -3 = y_o + 0 y_o = -3. The coordinates of the object are (-1,-3). The coordinates of the object are (-1,-3). 17. A bag contains 8 red balls and 6 blue balls all identical in size and shape. Jane selected 3 balls at random without replacement. (a) Draw a tree diagram to represent this information. Step 1: Identify initial probabilities. Total number of balls = 8 Red + 6 Blue = 14 balls. Probability of drawing a Red ball first (R1) = (8)/(14) Probability of drawing a Blue ball first (B1) = (6)/(14) Step 2: Draw the tree diagram for three selections without replacement. ` Start | ___________________________|___________________________ / \ / \ (8/14) R1 (6/14) B1 / \ / \ / \ / \ / \ /___________________________ ___________________________\ / \ / \ / \ / \ (7/13) R2 (6/13) B2 (8/13) R2 (5/13) B2 / \ / \ / \ / \ / \ / \ / \ / \ R3 (6/12) B3 (6/12) R3 (7/12) B3 (5/12) R3 (7/12) B3 (5/12) R3 (8/12) B3 (4/12) `