1. Problem of The Day
A vector v of length 6 makes a 150 degree angle with the vector [1,0], when they are placed tail-to-tail. Find the components of v.

2. Distance between a point and a line
Objective: To be able to find the distance between a point and a line
TS: Making decisions after reflection and review
Warm up:
Write y= (1/2)x - (3/2) in general form

3. To find the distance between a point (x1, y1) and a line whose general form is Ax + By + C = 0 (where A, B & C must be integers), you can use the formula
where d is the shortest (perpendicular) distance between the point and the line.
For example:
To find the distance between a point (2, 4) and the line y = ½ x – 3/2, I would first get the line into general form:
2y = x – 3
0 = x – 2y – 3
So A = 1, B = -2 and C = -3
Now I would plug into the formula to find the distance between the point and the line
This means your first step is to identify a point you’re measuring from and the equation (in general form, Ax + By + C = 0) of the line you’re measuring to.

4. Find the distance from the point to the line:
1. (4, -1) and 4x + 3y – 6 = (1, 5) and 5x – 12y + 7 = 0
3. (-1, 2) and 3x + y + 8 = (0, 3) and -2x + 5y – 6 = 0

5. 5. 4x – 5y + 8 = 0 6. 2x + 7y + 5 = 0 4x – 5y + 2 = 0 2x + 7y – 3 = 0
Find the distance between the parallel lines:
5. 4x – 5y + 8 = x + 7y + 5 = 0
4x – 5y + 2 = x + 7y – 3 = 0

6. A line is parallel to 3x – 4y = 6, and 3 units from the origin
A line is parallel to 3x – 4y = 6, and 3 units from the origin. Find the equation of the line.

7. A line is parallel to the line through A(-6, 2) and B(6, 7) and is tangent to the circle with center at the origin and radius of 5. Find the equation of the line.

8. Find the distance between 3x- 6y- (7/2) and -2x + 4y +5=0

9. In triangle ABC, find the lengths of the three altitudes
In triangle ABC, find the lengths of the three altitudes. A(-5, -2) B(1, 6) C(7, 3)