Given that the coordinates of point P (x, y) satisfy the condition x + y ≤ 4Y ≥ XX ≥ 1, and point O is the origin of coordinates, then the minimum value of | Po | is equal to___ , the maximum value is equal to___ ．

Given that the coordinates of point P (x, y) satisfy the condition x + y ≤ 4Y ≥ XX ≥ 1, and point O is the origin of coordinates, then the minimum value of | Po | is equal to___ , the maximum value is equal to___ ．

Draw the feasible region, as shown in the figure: easy to get a (2,2), OA = 22b (1,3), OB = 10; C (1,1), OC = 2, so the maximum value of | op | is 10, and the minimum value is 2

Given the line l1:2x + y-6 = 0 and point a (1, - 1), the equation of line l can be obtained by crossing point a as the line L and L1 intersect at point B, and the absolute value of AB = 5
A high school mathematics problem, please give us more guidance. Need detailed process, thank you
Note: 1 in L1 is a subscript

Let the equation of the line l be: y = KX + B ∵ the line L passes through the point a (1, - 1); - 1 = K + B → B = - 1-k, that is, y = kx-1-k ∵ the line L and L1 intersect at the point B, ∵ kx-1-k = 6-2x → x = (7 + k) / (K + 2) ∵ y = 6-2x = 6-2 [(7 + k) / (K + 2)] = (4k-2) / (K + 2) the coordinates of point B ((7 + k) / (K + 2), (4k-2) / (k

As shown in the figure, point a (0,4), point B (3,0), point P is a moving point on the line AB, make PM ⊥ Y axis at point m, make PN ⊥ X axis at point n, connect Mn, when point P moves to what position, the value of Mn is the minimum? What is the minimum value? Find out the length of PN at this time

As shown in the figure, connect op. it is known that:  PMO =  mon =  ONP = 90 °. The quadrilateral onpm is a rectangle.  OP = Mn. In RT △ AOB, when op ⊥ AB, OP is the shortest, that is, Mn is the smallest.  a (0,4), B (3,0), that is, Ao = 4, Bo = 3. According to the Pythagorean theorem, ab = 5.  s △ AOB = 12ao · Bo = 12ab · OP,  OP = 125.  Mn = 125. That is, when point P moves to make op ⊥ AB at point P, Mn is the shortest In RT △ POB, according to Pythagorean theorem, BP = 95, ∵ s △ OBP = 12op · BP = 12ob · PN. ∵ PN = 3625

It is known that the three strings AB, CD and EF in circle O intersect at P, P is the midpoint of AB, CF intersects AB at m, de intersects AB at n, and the proof is PM = PN
This problem seems to be called Butterfly Theorem

Here's a concrete proof. Let's see if it's the same

As shown in the figure, the length of line segment AB is 1. (1) the point C on line segment AB satisfies the relation ac2 = BC × AB to find the length of line segment AC. (2) the point D on line segment AC satisfies the relation ad2 = CD × AC to find the length of line segment ad; (3) the point D on line segment ad satisfies the relation AE2 = de × ad to find the length of line segment AE?

(1)AC=(5^(1/2)-1)/2
(2)AD=((5^(1/2)-1)/2)^2
(3)Ae=((5^(1/2)-1)/2)^3
The law is very obvious. Find it yourself

As shown in the figure, if B and C are two points on the line ad, and ab: BC: CD = 3:2:4, EF is the midpoint of AB and CD respectively, EF = 22cm, calculate ad

Let AB = 3x, BC = 2x, CD = 4x
∴FB=3X/2 CF=4X/2=2X
∴EF=FB+BC+CF
22=(3X/2)+2X+2X
22=11X/2
X=4
∴AB=3*4=12 BC=2*4=8 CD=4*4=16
∴AD=AB+BC+CD=12+8+16=36

As shown in the figure, BC is the two points on the line ad, and ab: BC: CD = 3:2:5, e and F are the midpoint of ABCD, and EF = 24 ab.bc.cd The length of

Let AB = 3x, BC = 2x, CD = 5x, then be = 3 / 2x, CF = 5 / 2x, then 3 / 2x + 2x + 5 / 2x = 24, x = 4,
∴AB=12,
∴BC=8,CD=20．