## Taylor Form

##### Warning: Sometimes these lines may not appear to be perpendicular. Many graphing calculator windows are not square, but instead rectangular. If windows are not square, the lines with negative reciprocal slopes will not appear perpendicular.

Periodically in Calculus you must recall the Distance Formula, the midpoint of a segment, and the angle of elevation.

## Distance Between Two Points

The distance, d, between (x1,y1) and (x2,y2) is

 The distance between (3,4) and (-5,8) is        or

## Midpoint of a Line Segment

If   and  are the end points of a line segment, then the midpoint of the line segment is

 Let (-2,4) and (-8,6) be endpoints of a line segment. To find the midpoint of the segment you can average the ordered pairs for the endpoints:    (-3,5)

Angle of Elevation

If a non-vertical line l intersects the x-axis at an angle t and has a slope of m then tan t = m.

 The line y = (x + 2) + 2, which is the Taylor form for y = x + 4, has a slope of 1 and intersects the x-axis at , therefore . So the angle of elevation for this line is .

##### 7. Write the equation, in Taylor form, of a line parallel to 3x - 2y = 7 that passes through (3,1). Enter this equation in your calculator and check to see that (3,1) is a solution to your equation.

8.  Find the distance between (-2,6) and (4,8)

9.  Find the midpoint of the line segment whose endpoints are (-2,6) and (4,8).

10.  Find the angle of elevation for the line