A plane passes through the point - 2 , - 2,2 and contains the line joining the points 1 , - 1,2 and 1,1 , 1 . Then the image of - 7,2 , 3 in the plane is

Question

A plane passes through the point - 2 , - 2,2 and contains the line joining the points 1 , - 1,2 and 1,1 , 1 . Then the image of - 7,2 , 3 in the plane is, 1 , - 1,5, - 5 , - 4 , - 2, - 6 , - 1 , - 3, 13 23 , 7 23 , 6 23

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The plane passes through the points - 2 , - 2,2 , 1 , - 1,2 , 1,1 , 1 Its equation is x + 2 y + 2 z - 2 3 1 0 3 3 - 1 = 0 ⇒ x - 3 y - 6 z + 8 = 0 Image of - 7,2 , 3 in the plane is x + 7 1 = y - 2 - 3 = z - 3 - 6 = - 2 - 7 - 6 - 18 + 8 1 + 9 + 36 x + 7 1 = y - 2 - 3 = z - 3 - 6 = 23 23 = 1 x = - 6 , y = - 1 , z = - 3

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