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Find the reflection of the point (alpha,...

Find the reflection of the point `(alpha, beta, gamma)` in the XY-plane, YZ-plane and ZX plane.

Text Solution

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Let P`(alpha, beta, gamma)` be the given point and also let Q(a, b, c) be its reflection point in XY-plane.
Let R be the point where PQ intersect XY-plane.
Then PQ is perpendicular to
XY-plane and R is the middle
point pf PQ.
`therefore` z-coordinate of R is 0
`rArr gamma + c = 0`
`rArr c = - gamma`
`therefore` coordinates of Q`(alpha, beta, -gamma)`
Similarly, image of point P`(alpha, beta, gamma)` in the YZ-plane is `(-alpha, beta, gamma)` and image of point P(`(alpha, beta, gamma)` in
the XZ-plane is `(alpha, -beta, gamma)`
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