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Given (1, 4) and (2, 6)
calculate 8 items:
Slope (m) = | y2 - y1 |
x2 - x1 |
Slope (m) = | 6 - 4 |
2 - 1 |
Slope (m) = | 2 |
1 |
Slope = 2
y - y1 = m(x - x1)
y - 4 = 2(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, 4) and the slope (m) = 2
b = 4 - (2 * 1)
b = 4 + 2
b = | 2 |
1 |
b = 2
y = 2x + 2
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((2 - 1)2 + (6 - 4)2)
D = Square Root((12 + 22))
D = √(1 + 4)
D = √5
D = 2.2361
Midpoint = |
x2 + x1 |
2 |
, |
y2 + y1 |
2 |
Midpoint = | |
1 + 2 |
2 |
, |
4 + 6 |
2 |
Midpoint = | |
3 |
2 |
, |
10 |
2 |
Midpoint = (3/2, 5)
Plot a 3rd point (2,4)
Our first triangle side = 2 - 1 = 1
Our second triangle side = 6 - 4 = 2
Using the slope we calculated
Tan(Angle1) = 2
Angle1 = Atan(2)
Angle1 = 63.4349°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 63.4349° = 26.5651
The y intercept is found by
Setting x = 0 in y = 2x + 2
y = 2(0) + 2
y = 2
Parametric equations are written as
(x,y) = (x0,y0) + t(b,-a)
(x,y) = (1,4) + t(2 - 1,6 - 4)
(x,y) = (1,4) + t(1,2)
x = 1 + t
y = 4 + 2t
x - x0 | |
z |
y - y0 |
b |
x - 1 | |
1 |
y - 4 |
2 |