Given (1, 42000) and (2, 39000)
calculate 8 items:
Slope (m) = | y2 - y1 |
x2 - x1 |
Slope (m) = | 39000 - 42000 |
2 - 1 |
Slope (m) = | -3000 |
1 |
Slope = -3000
y - y1 = m(x - x1)
y - 42000 = -3000(x - 1)
Standard equation of a line is y = mx + b
where m is our slope
x and y are points on the line
b is a constant.
Rearrange the equation to solve for b
we get b = y - mx.
Use (1, 42000) and the slope (m) = -3000
b = 42000 - (-3000 * 1)
b = 42000 - 3000
b = | 45000 |
1 |
b = 45000
y = -3000x + 45000
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((2 - 1)2 + (39000 - 42000)2)
D = Square Root((12 + -30002))
D = √(1 + 9000000)
D = √9000001
D = 3000.0002
Midpoint = |
x2 + x1 |
2 |
, |
y2 + y1 |
2 |
Midpoint = | |
1 + 2 |
2 |
, |
42000 + 39000 |
2 |
Midpoint = | |
3 |
2 |
, |
81000 |
2 |
Midpoint = (3/2, 40500)
Plot a 3rd point (2,39000)
Our first triangle side = 2 - 1 = 1
Our second triangle side = 42000 - 39000 = 3000
Using the slope we calculated
Tan(Angle1) = -3000
Angle1 = Atan(-3000)
Angle1 = -89.9809°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - -89.9809° = 179.9809
The y intercept is found by
Setting x = 0 in y = -3000x + 45000
y = -3000(0) + 45000
y = 45000
Parametric equations are written as
(x,y) = (x0,y0) + t(b,-a)
(x,y) = (1,42000) + t(2 - 1,39000 - 42000)
(x,y) = (1,42000) + t(1,-3000)
x = 1 + t
y = 42000 - 3000t
x - x0 | |
z |
y - y0 |
b |
x - 1 | |
1 |
y - 42000 |
-3000 |