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
105 Answers
Pour montrer que les lignes perpendiculaires tracées depuis les sommets d’un carré vers les côtés opposés sont concourantes en un point à l’intérieur du carré, nous pouvons utiliser la rotation géométrique. Considérons un carré ABCD contenant un point P. Nous montrerons que les droites perpendiculaires tracées 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 à BP. Appelons X l'intersection de cette ligne perpendiculaire et de BP. 2. Effectuons maintenant une rotation du carré de 90 degrés 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 mappé au segment de droite. CP. 3. Après la rotation, la droite perpendiculaire de C à CP coïncide avec la droite perpendiculaire d’origine de B à BP. Par conséquent, le carré pivoté ABCD a la même propriété : les droites perpendiculaires allant de B, C et D à CP, DP et AP, respectivement, se coupent également au point X. 4. Répétez le processus pour les sommets restants du carré. Effectuez successivement des rotations de 90 degrés dans le sens des aiguilles d’une montre autour des points B, C et D. Chaque rotation mappe le carré sur lui-même et préserve la propriété des lignes perpendiculaires concurrentes. Par conséquent, les lignes perpendiculaires allant de A, B, C et D à BP, CP, DP et AP, respectivement, se coupent toutes au point X, qui est le point d'intersection de toutes les lignes perpendiculaires pivotées. Ainsi, nous avons montré que les lignes perpendiculaires tracées depuis les sommets A, B, C et D du carré jusqu’aux côtés opposés BP, CP, DP et AP, respectivement, sont concourantes en un point à l’intérieur du carré.

Frequently asked questions (FAQs)
Find the sum of the first 10 positive integers.
+
Math Question: A car travels at a speed of 60 mph, how long will it take to cover a distance of 180 miles?
+
What is the formula for converting degrees to radians?
+
New questions in Mathematics
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?
-6(3x-4)=-6
For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight
X^2 = 25
A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.
A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.
2X+2=8
Calculate the change in internal energy of a gas that receives 16000 J of heat at constant pressure (1.3 atm) expanding from 0.100 m3 to 0.200 m3. Question 1Answer to. 7050J b. 2125J c. None of the above d. 2828J and. 10295 J
Find the vertex F(x)=x^2-10x
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
2p-6=8+5(p+9)
(3.1x10^3g^2)/(4.56x10^2g)
The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?