formula to calculate image of a point
kvnmurty:
This is a question in co-ordinate geometry.
Answers
Answered by
0
This is a question in co-ordinate geometry.
given straight line : L = a x + b y + c = 0 --- equation 1
slope = m1 = - a/b
We want to find the image of a point P (x1, y1) w.r.t. the above line L. Let the image be Q(x2,y2). Then the mid-point R of PQ lies on the line L. Also, PQ is perpendicular to L.
So slope of PQ = m2 = -1/m1 = b/a
So (y2 - y1) / b = (x2 - x1) / a = k (say) -- equation 2
Mid point R of PQ = [ (x1+x2)/2, (y1+y2)/2 ], This lies on L. so
a (x1+x2)/2 + b (y1+y2)/2 + c = 0 --- equation 3
Simplifying 3 and by using k from equation 2, we get,
k = - 2 (a x1+ b y1 + c) / (a² + b²)
x2 = a k + x1
y2 = b k + y1
given straight line : L = a x + b y + c = 0 --- equation 1
slope = m1 = - a/b
We want to find the image of a point P (x1, y1) w.r.t. the above line L. Let the image be Q(x2,y2). Then the mid-point R of PQ lies on the line L. Also, PQ is perpendicular to L.
So slope of PQ = m2 = -1/m1 = b/a
So (y2 - y1) / b = (x2 - x1) / a = k (say) -- equation 2
Mid point R of PQ = [ (x1+x2)/2, (y1+y2)/2 ], This lies on L. so
a (x1+x2)/2 + b (y1+y2)/2 + c = 0 --- equation 3
Simplifying 3 and by using k from equation 2, we get,
k = - 2 (a x1+ b y1 + c) / (a² + b²)
x2 = a k + x1
y2 = b k + y1
Attachments:
i hope it is easy to understand
Similar questions