Question

P 13. Let P a point inside of a square ABCD. Show that the perpendicular lines drawn from A, B, C, respectively D, to BP, CP, DP, respectively AP are concurrent. Use geometric rotation.

297

likes
1484 views

Answer to a math question P 13. Let P a point inside of a square ABCD. Show that the perpendicular lines drawn from A, B, C, respectively D, to BP, CP, DP, respectively AP are concurrent. Use geometric rotation.

Expert avatar
Gene
4.5
103 Answers
Pour montrer que les lignes perpendiculaires tracĂ©es depuis les sommets d’un carrĂ© vers les cĂŽtĂ©s opposĂ©s sont concourantes en un point Ă  l’intĂ©rieur du carrĂ©, nous pouvons utiliser la rotation gĂ©omĂ©trique. ConsidĂ©rons un carrĂ© ABCD contenant un point P. Nous montrerons que les droites perpendiculaires tracĂ©es respectivement de A, B, C et D vers BP, CP, DP et AP se coupent en un seul point. 1. Dessinez le segment de droite AP et construisez une ligne perpendiculaire de A Ă  BP. Appelons X l'intersection de cette ligne perpendiculaire et de BP. 2. Effectuons maintenant une rotation du carrĂ© de 90 degrĂ©s dans le sens des aiguilles d'une montre autour du point A. Cette rotation mappe le point B au point C, le point C au point D et le point D au point P. Le segment de droite BP est mappĂ© au segment de droite. CP. 3. AprĂšs la rotation, la droite perpendiculaire de C Ă  CP coĂŻncide avec la droite perpendiculaire d’origine de B Ă  BP. Par consĂ©quent, le carrĂ© pivotĂ© ABCD a la mĂȘme propriĂ©té : les droites perpendiculaires allant de B, C et D Ă  CP, DP et AP, respectivement, se coupent Ă©galement au point X. 4. RĂ©pĂ©tez le processus pour les sommets restants du carrĂ©. Effectuez successivement des rotations de 90 degrĂ©s dans le sens des aiguilles d’une montre autour des points B, C et D. Chaque rotation mappe le carrĂ© sur lui-mĂȘme et prĂ©serve la propriĂ©tĂ© des lignes perpendiculaires concurrentes. Par consĂ©quent, les lignes perpendiculaires allant de A, B, C et D Ă  BP, CP, DP et AP, respectivement, se coupent toutes au point X, qui est le point d'intersection de toutes les lignes perpendiculaires pivotĂ©es. Ainsi, nous avons montrĂ© que les lignes perpendiculaires tracĂ©es depuis les sommets A, B, C et D du carrĂ© jusqu’aux cĂŽtĂ©s opposĂ©s BP, CP, DP et AP, respectivement, sont concourantes en un point Ă  l’intĂ©rieur du carrĂ©.

Frequently asked questions (FAQs)
What are the key characteristics of the cotangent function f(x) = cot x?
+
What is the sine value of an angle in a trigonometric table if it is provided with an angle measure?
+
Math question: What is the square root of 384756121
+
New questions in Mathematics
431414-1*(11111-1)-4*(5*3)
The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?
1. Suppose we have a good whose quantity supplied changed from 100 to 120 units when the price increased from $10 to $12 per unit. Compute the price elasticity of supply using the midpoint method
An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.
224 × (6Ă·8)
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?
Find the sum of the first 41 terms of the progression that begins: 32, 24, 16, 

The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers
How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
The equation of the straight line that passes through the coordinate point (2,5) and is parallel to the straight line with equation x 2y 9 = 0 is
12(3+7)-5
v Is the following statement a biconditional? If Shannon is watching a Tigers game, then it is on television.
7. Find the equation of the line passing through the points (−4,−2) 𝑎𝑛𝑑 (3,6), give the equation in the form đ‘Žđ‘„+𝑏𝑩+𝑐=0, where 𝑎,𝑏,𝑐 are whole numbers and 𝑎>0.
In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?
(2m+3)(4m+3)=0
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
2X+2=8
A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?
Let I be an interval and let f : I → R be a continuous function such that f(I) ⊂ Q. Show (in symbols) that f is constant.
Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.