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Find the reflection of the point (1,2,-1) in the plane 3x-5y+4z = 5

Find the reflection of the point (1,2,-1) in the plane 3x-5y+4z = 5

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
Line normal to given plane is (x-1)/3=(y-2)/-5=(z+1)/4
Writing y and z in terms of x we get
y=(-5x+11)/3
z=(4x-7)/3
Substituting the above equations in given plane equation we get
x=49/25
y=2/5
z=7/25
To find the reflected point
we use mid point formula
(1+a)/2=(49/25)
so a=83/25
(2+b)/2=2/5
so b=-6/5
(-1+c)/2=7/25
so c=39/25
So the reflected point is (83/25,-6/5,39/25)

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