Derivation process of distance formula from point to straight line
Definition forensics: According to the definition, point P(x? ，y？ ) Distance to straight line L: ax+by+c = 0 is the vertical length from point P to straight line L. Let the vertical line from point P to straight line L be L' and the vertical foot be Q, then the slope of L' is B/A, and the analytical formula of L' is y-y? =(B/A)(x-x？ The coordinates of the intersection q of l and l' are ((B^2x? Abby? -AC)/(A^2+B^2)，(A^2y？ -ABx？ -BC)/(A 2+B 2)) From the distance formula between two points:
PQ^2=[(B^2x？ Abby? -AC)/(A^2+B^2)-x0]^2
+[(A^2y？ -ABx？ -BC)/(A^2+B^2)-y0]^2
=[(-A^2x？ Abby? -AC)/(A^2+B^2)]^2
+[(-ABx？ -B^2y？ -BC)/(A^2+B^2)]^2
=[A(-By？ -C-Ax？ )/(A^2+B^2)]^2
+[B(-Ax？ -C-By？ )/(A^2+B^2)]^2
=A^2(Ax？ +By？ +C)^2/(A^2+B^2)^2
+B^2(Ax？ +By？ +C)^2/(A^2+B^2)^2
=(A^2+B^2)(Ax？ +By？ +C)^2/(A^2+B^2)^2
=(Ax？ +By？ +C)^2/(A^2+B^2)
So PQ=|Ax? +By？ +c |/√ (a 2+b 2), formula proof.
Extended Reading: How to Remember Mathematical Formulas
1, chain storage method
It is to connect the words to be memorized one by one and think of another from one word. The key to this memory lies in the firmness of the chain connected in series. For example, let's remember three groups of words: desk, basketball and tall building. First, the desk and basketball are linked, and the basketball under the desk gradually becomes bigger. Push the desk to the roof, then basketball and tall buildings fall from the sky and hit the tall buildings.
2, the story memory method
First, key words are extracted from the content to be memorized, and then the key words are connected in series through vivid stories to help memory.
3. Pile method
First, use fixed piles, such as body piles, digital piles and Roman houses. And then link the memory content with the pile to achieve the purpose of memory.
4, formula memory method
Use formulas and slips, such as 185 1, Jintian Xiuquan Uprising, 1839.6.3, Lin Zexu's smoke in Humen Beach, etc.
5, the first letter memory method, extracting the first letter to reduce the memory burden.
6, inductive memory method, the same content memory, according to the principle of brain storage.
7, chart memory method, you need to remember the content of the image, using the right brain to help remember.
8, music memory method, using A-band music, mobilize the subconscious to help remember.
9. Repeat the memory method, try to remember and help you remember.
10, associative memory method, using homophonic and other means to assist memory.