A two digit ten digit is x and a single digit one. After the transposition, the new two digit is 18 smaller than the original one. Which equation should X be and what is x

10x+1-18=10+x
9x=27
x=3

As shown in the figure, there are two points P1 (x1, Y1) and P2 (X2, Y2) on the image of hyperbola y = K / X (k > 0, x > o), and X1 < x2. Make a vertical line through P1 and P2 to the x-axis, and the perpendicular feet are B and D. make a vertical line through P1 and P2 to the y-axis, and the perpendicular feet are a and C. If you remember that the area of quadrilateral ap1bo and quadrilateral cp2do are S1 and S2, and the perimeter is C1 and C2, try to compare the sizes of S1 and S2, C1 and C2
Have a detailed process and answers

(1) According to the geometric meaning of inverse proportional function coefficient K, S1 = S2 = K;
When y1-y2 = x2-x1, that is, AC = BD, C1 = C2;
When y1-y2 < x2-x1, that is, AC < BD, C1 < C2;
When y1-y2 > x2-x1, namely AC > BD, C1 > C2

Given that the points P1 (x1, Y1), P2 (X2, Y2) are on the hyperbola y = - 2 / x, when x1

y2>Y1
You can draw a diagram of the inverse scale function by yourself, and then you can judge it. You can also prove mathematically that it's good to use y1-y2 = to bring in the general division and subtraction

For any two points P1 (x1, Y1) and P2 (X2, Y2) in the plane rectangular coordinate system, we call | x1-x2 | + | y1-y2 | the rectangular distance between P1 and P2 as D (P1, P2)
Given that O is the coordinate origin and the coordinates of point P are (2, - 3), then d (O, P) = ()
A 2 B 5 C 3 D -5
Thank you for the specific steps

Answer B
So D (O, P) = | 2-0 | + | - 3-0 | = 2 + 3 = 5

For any two points P1 (x1, Y1) and P2 (X2, Y2) in the plane rectangular coordinate system, we call | x1-x2 | + | y1-y2 | the rectangular distance between P1 and P2 as D (P1, P2)
Given that O is the origin of coordinates, and the moving point P (x, y) satisfies D (O, P) = 1, please write the relationship between X and y
The answer is | x | + | y | write | - x | + - | y | right? The results of the two formulas are the same. O = 0-x = - X. P = 0-y = - y, right? That's why I write that answer

Topic meaning
|x|+|y|=1
① When x > 0, Y > 0, x + y = 1
②x>0, y

There is a problem in our homework: in the plane rectangular coordinate system, there are P1 (x1, Y1), P2 (X2, Y2), known as p1p2 = | x2-x1 |,
Where is line p1p2? (x-axis or something)

Satisfy Y1 = Y2, that is to say, those parallel to the X axis are
The calculation results are as follows:
P1p2 = radical [(x2-x1) ^ 2 + (y2-y1) ^ 2] = | x2-x1|
Square of both sides to get (x2-x1) ^ 2 + (y2-y1) ^ 2 = (x2-x1) ^ 2, so (y2-y1) ^ 2 = 0 to get y2 = Y1

In Cartesian coordinates, O is the origin of coordinates, P1 (x1, Y1), P2 (X2, Y2) are the two points in the first quadrant. If 1, x1, X2, 4 are in equal difference sequence, and 1, Y1, Y2, 8 are in equal proportion sequence, then the area of △ op1p2 is ()
A. 1B. 2C. 3D. 4

Analysis: according to the properties of the arithmetic and proportional sequence, we can see that X1 = 2, X2 = 3, Y1 = 2, y2 = 4. P1 (2, 2), P2 (3, 4); {OP1} = 22, {op2} = 5, {sin} p1op2 = 1 − (7210) 2 = 210} s △ O & nbsp; P1 & nbsp; P2 = 12 × 22 × 5 × 210 = 1, so we choose a

P1 (x1, Y1), P2 (X2, Y2), if p1p2 = (x2-x1), (bracket means absolute value), then the position of p1p2
P1 (x1, Y1), P2 (X2, Y2), if p1p2 = "x2-x1), then the position of p1p2 is a. p1p2 must be on X-axis B. p1p1 must be on Y-axis C. p1p2 is parallel to x-axis or p1p2 is on X-axis D. p1p2 is parallel to Y-axis or p1p2 is on y-axis

Then the position of p1p2 is c. p1p2 is parallel to the X axis or p1p2 is on the X axis

Given the points P1 (x1, Y1), P2 (X2, Y2) and the line L: ax + by + C = 0, the line segment p1p2 intersects the line L at point P
If the sum of the points is not coincident with the whole line (p 1 + p 2, p 1 + y 2) and the line is known to be P1 0 + y 2 (p 1 + p 2)
① Verification: = - (ax1 + by1 + C) / (AX2 + BY2 + C)
② If P1 (1,4), P2 (5,1), line y = K (2x-3) + 4 intersects line p1p2 at P, the value range of K is obtained
The process, please

Because vector p1p = Λpp2 (P and P2 do not coincide)
From the formula of fixed score point, let P (x0, Y0)
x0=(x1+∧x2)/(1+∧)
y0=(y1+∧y2)/(1+∧)
On the straight line, there are:
ax0+by0+c=0
a(x1+∧x2)+b(y1+∧y2)+c(1+∧)=0
ax1+by1+c=-∧(ax2+by2+c)
The proof of Λ = - (ax1 + by1 + C) / (AX2 + BY2 + C)
P is on line p1p2, so Λ is greater than 0
The straight line is K (2x-3) + 4-y = 0
∧=-(k(2-3)+4-4)/(k(10-3)+4-1)
=k/(7k+3)>0
k0

Given that the equation of the line L is f (x, y) = 0, and the points P1 (x1, Y1) and P2 (X2, Y2) are on L and out of L respectively, then the equation f (x, y) - f (x1, Y1) - f (X2, Y2) = 0
Denoted as a line passing through P2 and parallel to L
Why does it mean P2?

∵ P1 (x1, Y1) on L
∴f(x1,y1)=0
The equation f (x, y) - f (x1, Y1) - f (X2, Y2) = 0 becomes:
f(x,y)-f(x2,y2)=0
Substituting x = X2, y = Y2 into the above formula holds, and the equation passes through P2

A two digit ten digit is x and a single digit one. After the transposition, the new two digit is 18 smaller than the original one. Which equation should X be and what is x