![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
As shown in the figure, it is known that the straight line M: y = - 1 / 2x + B intersects with the X axis at a (15,0). Take OA as one side, make a rectangle oabc, B in the first quadrant As shown in the figure, it is known that the straight line M: y = - 1 / 2x + B intersects with the X axis at a (15,0). Take OA as one side, make a rectangle oabc in the first quadrant. BC intersects with the straight line m at point D, connecting OD, and od is perpendicular to the straight line M. (1) calculate the length of OD (2) Fold the rectangle along a straight line n so that point B falls on the coordinate axis F and connect BF. Let BF intersect with the straight line n at point P. if point P just falls on the straight line m, calculate the coordinates of point F
one
Substituting a (15,0) into the expression of the straight line m, we can get b = 15 / 2
So m: y = - 1 / 2x + 15 / 2
Because od is perpendicular to M
So the slope of OD = 2
So od: y = 2x
Because D is the intersection point of OD and m, we can solve the equations: x = 3, y = 6, that is, D (3,6)
So the length of OD = 3 √ 5
two
According to the calculation in 1, B (15,6)
Because B and F are symmetric with respect to line n, BF and line n intersect at point P
So p is the midpoint of BF
When f is on the x-axis, Let f (F, 0)
So the abscissa of point P = (15 + F) / 2, and the ordinate of point P = 6 / 2 = 3
Because P is a point on M
So 3 = - (15 + F) / 4 + 15 / 2
f=3
So f (3,0)
When f is on the y-axis, Let f (0, f)
So the abscissa of point P = 15 / 2 and the ordinate = (6 + F) / 2
Because P is a point on M
So 3 + F / 2 = - 15 / 4 + 15 / 2
f=3/2
So f (0,3 / 2)
RELATED INFORMATIONS
- 1. Given the equation x ^ 2-4x + 5 + a (1 / 2 of x) = 0, if a is a positive real number, then the following judgment is correct A. There are three unequal real roots B. There are two unequal real roots C. There is one real root d. There are no real roots
- 2. Three judgment questions in exercises of prime number and composite number 1) (2) 3 is a divisor and 12 is a multiple 3) 16 is a multiple of 16 and a divisor of 16. 4) 1 is a divisor of any natural number 5) Because 5 △ 2 = 2.5, 5 is a multiple of 2 and 2 is a divisor of 5 6) 0 is a natural number and also an integer. () 7) 48 is divisible by 6, and 48 is divisible by 6 8) The divisor of a number is always smaller than the multiple. (9) natural numbers can be divided into prime numbers and composite numbers according to the number of divisors 10) The number of bits divisible by 3 is 3, 6, 9. (11) 29 is divisible by 5 12) 21 △ 7 = 3, 21 is a multiple, 7 is a divisor. (13) because 2.8 △ 0.7 = 4, 2.8 can be divided by 0.7 14) 15) odd plus odd, sum must be even 16) Even number × odd number = even number () 17) even numbers greater than 2 are composite numbers 18) Even numbers are composite numbers, prime numbers are odd numbers. () 19) the product of two prime numbers must be composite numbers 20) The sum of two prime numbers must be a composite number Fill in "right" or "wrong" in parentheses. Write down some controversial questions and your reasons For example; 13) Because 2.8 △ 0.7 = 4, 2.8 can be divided by 0.7 If right, why right, if wrong, why wrong, explain
- 3. The prime number has at most two factors, and the combined number has at least three factors Prime number has 2 factors at most, total number has 3 factors at least, judge right or wrong fast!
- 4. The sum of two prime numbers must be a composite problem
- 5. Judgment questions 1, 0 are even numbers () 2, 2 are composite numbers () 3, 1 is the smallest prime number () 4, in three digits, the smallest prime number is 101 () 5. A nonzero number with at least two divisors () 6. Prime number is prime factor () 7. 9 and 6 are the prime factors of 54 () Check right, cross wrong
- 6. From 1 to 10, the total numbers are 4, 6, 8, 9 and 10, and the rest are prime numbers______ ．
- 7. 1, 2, 3, 4 and 9 are odd and prime numbers, even numbers are not composite numbers, even numbers are composite numbers, even numbers are composite numbers. Give me 60 minutes
- 8. Who are prime numbers? Who are composite numbers? Who are odd numbers? Who are natural numbers?
- 9. The sum of not even numbers within 20 is () and the prime of not odd numbers is ()
- 10. 1. Which of the numbers 2, 3, 7, 9, 15, 78, 150 are composite numbers in odd numbers and which are prime numbers in even numbers
- 11. If the parameter equation of the line L is x = 1 + 3ty = 2-4t (t is the parameter), then the cosine of the inclination angle of the line L is___ ．
- 12. The first question of x ^ 3-3ax ^ 2-9a ^ 2x-a ^ 3, when a = 1, is to find the extremum. The answer is derivative. I can't understand it, I study literature, so I'd better hurry up and have no requirements. There should be no problems for people above grade three in senior high school, so I don't give too many rewards. To promote the ideological and moral construction, we should take serving the people as the core, collectivism as the principle, focus on improving the sense of honesty, love the motherland, love the people, love labor, love science, love socialism as the basic requirements, and social morality and professional ethics as the core, Focusing on family virtues and personal morality, we should carry out the party's basic theory in depth~
- 13. The symmetry axis of parabola y = x ^ 2-5 (M + 1) x + 2m is Y axis,
- 14. My favorite fruit is banana?
- 15. Find the slope and inclination angle of the straight line passing through points a (3.5) and B (A.2)
- 16. 12. The greatest common factor and the least common multiple of 16 and 30 24、16、18、 14、21、42、 22、77、42、 Say pull down, use short method, step by step, how to seek
- 17. As shown in the diamond ABCD in the figure, ∠ ABC = 120 °, f is the midpoint of DC, the extension line of AF intersects the extension line of BC at e, then the degree of the acute angle between the straight line BF and the straight line De is () A. 30°B. 40°C. 50°D. 60°
- 18. The two numbers are composite numbers, and their greatest common factor and least common multiple are 1 and 120 respectively?
- 19. If OA vector and ob vector are not collinear, let om vector = λ OA vector + μ ob vector (λ, μ∈ R) prove: if a, B and m are collinear, then λ + μ = 1
- 20. To sum up, which words are in the same line? There are special plural changes The more, the better,