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The distance between points Find point P on the coordinate axis so that PA = Pb, a (- 5,2), B (- 1,7)
Should not be a point? It seems to be a straight line
Draw a graph, two points a and B, and make the vertical bisector of the line segment. You can find the slope of AB (5 / 4), and then find the midpoint
How to find the distance from the point to the point in space?
D = root (x ^ 3 + y ^ 3 + Z ^ 3)
Point to point distance formula ~ point to line distance formula~
If a (a, b) B (C, d), then the distance from point a to point B is
Suppose we find the distance from C (a, b) to the line L1: y = KX + H, because it is the distance from the point to the line, we should make the vertical line L2 of the line through the point C, then the obtained line L2 is perpendicular to y = KX + H, then the slope of the line is - 1 / K (because the product of the slopes of two mutually perpendicular lines is - 1, that is K1 * K2 = - 1). Knowing the slope of the line and the point it wants to pass through, then the line L2 can be obtained, If we find out the intersection D of L1 and L2, we can find out the distance between point C and point D
What is the image with fixed distance from moving point to point and straight line
That is, if a focus of the ellipse becomes a straight line
The circle establishes a rectangular coordinate system, sets the fixed point as the origin, and sets the fixed line as x = a (such a coordinate system can always be designed, as long as the coordinate axis is rotated around the origin), so the moving point (x, y) has x ^ 2 + y ^ 2 + / x-a / = m (M is the fixed value)
So for a circle, we can further discuss the value of M, which may be the degenerate form of a circle
Find the distance between different lines, the formula of the distance from point to surface. Thank you
Distance formula of out of plane straight line d = [AB * n] / [n] (AB is the line connecting any two points of out of plane straight line, n is the normal vector, bracket is the module of vector)
The distance from point to plane is any point B in the plane, the plane normal vector is n, the distance from point a to the plane is n
d=【AB*n】/【n】
Distance formula of point and plane
Vector formula
Let the coordinates of the point (x0, Y0, Z0). Plane a (x-a) + B (y-b) + C (z-c) = 0 (or ax + by + CZ + D = 0), then the distance from the point to the plane is: | ax0 + by0 + CZ0 + D | / √ (x0 ^ 2 + Y0 ^ 2 + Z0 ^ 2). Where (a, B, c) is the normal vector of the plane
What's the point of triangle center of gravity?
In geometry, the meaning of the center of gravity of a triangle is: the intersection of the three central lines of a triangle. Its original meaning has nothing to do with the center of gravity of physics
Physical meaning of triangle center of gravity
When lifting the triangle with a rope, no matter where the rope is tied, the rope or its extension line will pass through a fixed point - the center of gravity
If you know the coordinates of the three vertices of a triangle, how can you find the coordinates of the center of gravity?
The center of gravity of a triangle is the sum and division of three coordinates
In triangle ABC
A(X,Y) B(P,Q) C(J,K)
Abscissa of center of gravity = (x + P + J) / 3
Ordinate of gravity center = (y + Q + k) / 3
If the vertex coordinates of the triangle are known, the coordinates of the center of gravity of the triangle can be obtained
The center of gravity is the intersection point of the three center lines of a triangle. Several properties of the center of gravity: (remember, it can be used flexibly) 1. The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1.2. The area of the three triangles composed of the center of gravity and the three vertices of the triangle is equal. 3. The sum of the squares of the distance from the center of gravity to the three vertices of the triangle is the smallest
RELATED INFORMATIONS
- 1. It is proved that the sum of the vectors of the center of gravity of a triangle and the lines of its three vertices is a zero vector
- 2. Let the coordinates of the three vertices of the triangle ABC be (x1, Y1), (X2, Y2), (X3, Y3) respectively, and find the coordinates of the center of gravity g of the triangle ABC The coordinates of the three vertices of the triangle ABC are (x1, Y1), (X2, Y2), (X3, Y3). Find the coordinates of the center of gravity g of the triangle ABC, set up the design algorithm, and draw the flow chart,
- 3. What are the center, the perpendicular, the center and the center of gravity of the triangle?
- 4. How to judge the center of triangle
- 5. What is the nature of the center of gravity of a triangle
- 6. Given two angles and the opposite side of one angle, how to make a triangle
- 7. What is the center of gravity of a triangle? What are its properties?
- 8. The formula of area of isosceles trapezoid Don't talk to me about: (top bottom + bottom bottom) × height × 1 / 2 I want something special An isosceles trapezoid~ Especially about the diagonal
- 9. Area formula of isosceles trapezoid Wait for the trapezoidal Top 45 bottom 50 bottom angle 70 height!
- 10. What is the formula of perimeter and area of isosceles trapezoid? In isosceles trapezoid ABCD, if ad ∥ BC, AE ⊥ BC are equal to e, and AE = ad, BC = 3aD, then ∠ B is equal to?
- 11. As shown in the figure, in the plane rectangular coordinate system, point O is the coordinate origin, the edge of rectangle ABCD falls on the coordinate axis, a (0,3), C (4,0), and point F is a moving point on the line BC. (there are four questions in total. The fourth question is to compare the length of OE and of and find the original question.)
- 12. (1) A kind of disinfectant is made up of 1:5 ratio of disinfectant and water bank. How many kilograms of water are put into 10 kilograms of disinfectant? (2) The 314cm thin iron wire is just wound 10 times on a round iron bar. What is the radius of the cross section of the round iron bar?
- 13. A geometry problem in the third grade of junior high school In the circle O, the diameter AB intersects with the diameter CD, passing through three points a, O and B respectively to make the vertical line of CD, and the vertical feet are e, h and f respectively
- 14. Two elementary geometry problems 1. In rectangle ABCD, point O is the midpoint of AC, AC = 2Ab, extend AB to g, make BG = AB, connect go to intersection BC to e, extend go to intersection ad to point F, prove: quadrilateral aecf is diamond 2. Make three equilateral triangles △ abd, △ BCE, △ ACF on the same side of BC with △ ABC three times (1) Quadrilateral what is ADEF and why? (2) When △ ABC satisfies what condition, the quadrilateral ADEF is a rectangle (3) When △ ABC satisfies what conditions, the quadrilateral ADEF is a diamond, why? (4) When △ ABC satisfies what conditions, quadrilateral with a, D, e, F as vertex does not exist? Thank you~
- 15. Several mathematical geometry proof questions! In a known parallelogram, extend Da to F, make AF = AC, connect CF with ab at point E, angle ABC = 120 degrees, angle CEB = 45 degrees, BC = 2, and find the length of BD (which cannot be proved by similar triangle) It is known that in the quadrilateral ABCD, ad = BC, F and m are the midpoint of DC and ab respectively, the extension lines of AD and MF intersect at g, and the extension lines of MF and BC intersect at E It is known that in the triangle ABC, e is the midpoint of BC, ad is perpendicular to BC, the perpendicular foot is D, de = 1 / 2Ab Magic snow baby 22:50:10
- 16. It is known that the three vertices of △ ABC are a (0,3), B (1,5), C (3, - 5). (I) find the linear equation of edge AB; (II) find the linear equation of middle line ad
- 17. The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?
- 18. tan22.5°1-tan222.5°= ___ ．
- 19. Set proof: Let the set {a = a | a = 3N + 2, n ∈ Z} and the set B = {B | B = 3K-1, K ∈ Z}, prove that a = B
- 20. The functional relationship between price f (T) and time t of a commodity in recent 30 days is f (T) = t + 10 (0