# Angles and distances

The **distance between two points**, *A(a _{1},a_{2})* and

*B(b*, is the magnitude of the vector

_{1},b_{2})*AB*:

The **distance between a point and a straight line**, *A(a _{1},a_{2})* and

*r:Ax + By + C = 0*, is:

The **distance between two parallel straight lines**, *r* and *s*, is the distance between a point in one of them and the other line: *d(r,s)=d(A,s)=d(B,r)*

The **angle between two straight lines**, *r* and *s*, is:

Example:

The coordinates of the middle point of a segment AB, where A(a1,a2) and B(b1,b2), is:

**Exercises**:

1.- Calculate the middle point of the segment *AB*, where *A(1,1), B(3,8)*

2.- If *A(3,3)*, *r: x + 3y + 7 = 0; s: 2x + 6y + 7 = 0; t: 2x - y = 0*; calculate:

a) *d(A,r)*

b) *d(r,s)*

c) The angle between *r* and *t*

* *

* *

* *

* *

Solutions: 1.-* M(2,9/2); *2.- a) 6*u; *b) 1.1*u; c) *98º7'48''

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