I was talking with a student today about the reflection of a line in a line, where both lines are in the same plane (naturally). And I thought of sharing it. One reason why I decided to discuss this in class was also because A’levels has been moving towards questions that want students to engineer their own solutions and thought process from start to end. So here it is a question. 🙂 Students can try first before clicking solution.
Given 
and 
. Find, in terms of 
and 
, the vector equation of the line 
, which is the reflection of 
about 
, in the same plane.
and have that 
is a point, 
on 
be the point of reflection of 
. Then 
for some 
.
Students might want to try to ask themselves, if the lines do not intersection 
instead, how does that change the approach? Assuming, they will still intersect somewhere.
