1
0
mirror of https://gitlab.com/magicalsoup/Highschool.git synced 2025-01-23 16:11:46 -05:00

Update Unit 1: Analytical Geometry.md

This commit is contained in:
James Su 2019-09-25 17:19:17 +00:00
parent e3571ebdc2
commit 68b8841d68

View File

@ -106,12 +106,9 @@ The orthocenter of a triangle is the common intersection of the 3 lines containi
## Ratios
- To calculate each segment of the line given the ratio, the answer is simply
- $`(x_1 + \dfrac{x_2 - x_1}{r}, y_1 + \dfrac{y_2 - y1}{r})`$, where $`r, (x_1,y_1) (x_2,y_2)`$ are the **total** ratio, first point and second point respectively.
- Note that the above is for moving up a line. When moving down, we simply subtract like so:
- $`(x_2 - \dfrac{x_2 - x_1}{r}, y_2 - \dfrac{y_2 - y1}{r})`$
- For example, from a point like $`(2, 3)`$ to a point ($`5, 6)`$, and having a ratio of $`2:1`$ split at point $`P`$, the coordindates of point $`P`$ is simply
- $`(5 - \dfrac{5-2}{3}, 7 - \dfrac{6-3}{3})`$
- Which is $`(4, 6)`$
- $`(x_1 + \dfrac{p(x_2 - x_1)}{r}, y_1 + \dfrac{p(y_2 - y_1)}{r})`$, where $`r, (x_1,y_1) (x_2,y_2), p`$ are the **total** ratio, first point, second point and the amount of steps respectively.
- Note that the above is for moving up a line. When moving down from the upper point, we simply subtract like so:
- $`(x_2 - \dfrac{p(x_2 - x_1)}{r}, y_2 - \dfrac{p(y_2 - y_1)}{r})`$
## Shortest Distance From Point To a Line
- The shortest distance is always a straightline, thus, the shortest distance from a point to a line must be **perpendicular.**