Unit 4 - Activity 2

They give you two points A and B, the symmetrical of B regarding A is the point S, that verifies

(or else from a equivalent formula

We can also say that S is the point, just as A is the midpoint of segment SB.

Since then, A(a₁,a₂) and B(b₁,b₂), we have two possibilities to get the point S symmetrical of B with respect to A:

1) Making a translation of vector A according to vector – (or else according to vector ):

S = A + (–) = A + = A + (A – B) = A + A – B = 2A – B

2) Supposing that S has some unknown coordinates S(x,y) and calculating them imposing the conditions that A being midpoint of the segment SB. Since then, like we saw it in the previous activity:

from first previous equation we can get x, and form the second, y.