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Question
Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.
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Solution
The equation of the line is `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)`
The coordinates of the origin O are (0, 0, 0)
For x = 0, `(x - 2)/(1) = (0 - 2)/(1)` = –2
For y = 0, `(y - 4)/(2) = (0 - 4)/(2)` = –2
For z = 0, `(z + 4)/(-2) = (0 + 4)/(-2)` = –2
∴ Coordinates of the origin O satisfy the equation of the line.
Hence, the line passes through the origin.
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