Current Affairs JEE Main & Advanced

Image of a Point in a Plane

Category : JEE Main & Advanced

Let P and Q be two points and let \[\pi \] be a plane such that



(i) Line PQ is perpendicular to the plane \[\pi ,\] and



(ii) Mid-point of PQ lies on the plane \[\pi \].



Then either of the point is the image of the other in the plane\[\pi \].



To find the image of a point in a given plane, we proceed as follows



(i) Write the equations of the line passing through P and normal to the given plane as  \[\frac{x-{{x}_{1}}}{a}=\frac{y-{{y}_{1}}}{b}=\frac{z-{{z}_{1}}}{c}\].




(ii) Write the co-ordinates of image Q as \[({{x}_{1}}+ar,\,{{y}_{1}},\,+br,\,{{z}_{1}}+cr)\].



(iii) Find the co-ordinates of the mid-point R of PQ.



(iv) Obtain the value of r by putting the co-ordinates of R in the equation of the plane.



(v) Put the value of r in the co-ordinates of Q.

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