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Sequences And Series

Question
CBSEENMA11015019

The co-ordinates of the mid-point C of a line segment AB are (-1, -2, 1). If the co-ordinates of point A are (2, 1, -3), find the co-ordinates of B.

Solution

Let the co-ordinates of the other end B be space left parenthesis straight alpha comma space straight beta comma space straight gamma right parenthesis
∴ co-ordinates of mid-point of line segment
    AB are open parentheses fraction numerator straight alpha plus 2 over denominator 2 end fraction comma space fraction numerator straight beta plus 1 over denominator 2 end fraction comma space fraction numerator straight gamma minus 3 over denominator 2 end fraction close parentheses left right arrow space left parenthesis negative 1 comma space minus 2 comma space 1 right parenthesis
rightwards double arrow        fraction numerator straight alpha plus 2 over denominator 2 end fraction space equals space minus 1 space or space straight alpha space equals space minus 4
              fraction numerator straight beta plus 1 over denominator 2 end fraction equals negative 2 space or space straight beta space equals space minus 5
               fraction numerator straight gamma minus 3 over denominator 2 end fraction space equals space 1 space rightwards double arrow space straight gamma space equals space 5
Hence, point B is (-4, -5, 5)