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As shown in the figure, RT ABC is a piece of right-angled triangle paper placed in a plane Cartesian coordinate system, the point O coincides with the origin, the point A is on the X axis, the point C is on the Y axis, OC= 3, CAO=30°, the RT OAC is folded so that the OC edge falls on the AC edge, and the point O coincides with the point D and folds to CE

1: Find the analytic formula of the straight line where the crease CE is located.

2: Find the coordinates of the point d.

1) Analysis: RT AOC, AOC=90°, OC= 3, CAO=30°

aco=60°==>∠ace=∠eco=30°

dce≌⊿oce==>oe=de=1, oc=dc=√3, ce=2

Point e(-1,0),c(0, 3)==>k(ce)=( 3-0) (0+1)=3

The CE equation is y = 3x + 3

2) Analysis: Set d(x,y).

tana=cd/ad==>tan30°=√3/ad==>ad=3

a(-3,0)，ac^2=9+3==>ac=2√3

oc=dc=√3

d is the midpoint of AC.

x=-3/2,y=√3/2

d(-3/2,√3/2)

Solution:1In RT OAC, OC= 3, CAO=30° AOC=90°

oa= 3 ac = 2√3 ∠aco=60° c（0，√3） a (-3 ,0)

From the known coe cde eco= ecd= 30°

In RT OEC, OC= 3, OCE=30° EOC=90°

oe =1 e (-1 ,0)

Let the analytical formula of the straight line CE be y=kx+b, and k= 3 b = 3 by using the undetermined coefficient method

Therefore, the analytical formula is y = 3x+ 3

2.∵△coe∽△cde ∴ cd = co = √3

and ac=2 3 d is the midpoint of ac.

d (-3/2，√3/2)

∠oca=60

∠oce=30

oe*tan30=oe

oe=1 set the line oe: y=kx+ 3

Bringing in e(-1,0) gives the straight line y = 3x + 3

d((-3+0) 2,(0+ 3) 2) i.e. d(,-3 2).

A( 0)d is the midpoint of AC d( 3 2) ceo=30 e( 0)x+by+c=0 brought in CE coordinates.

3b+c=0

c=b=-√3/6

Analytic x-3 6y+

Dizzy: What grade is this? It's too simple to faint to death.

The diagonals of the diamond are bisected perpendicular to each other, so the side length of the diamond is ((24 2) 2+(10 2) 2).

13. The area of the diamond = side length * height = the product of the diagonal, set the height to h

13h=24*10/2=120

h=120/13

It's a parallelogram and it's a diamond.

Proof: Because of AB CD, CE AD, the quadrilateral AECD is a parallelogram. And there is an AC deuce bad, so.

AC bisects ECD, so the triangle AEC is all equal to the triangle ADC, so AE=AD, and the quadrilateral AECD is a parallelogram, there are AE=CD, CE=AD, so the quadrilateral AECD quadrangle is equal and is a diamond.

a+1) (b) Row seepage = ab+b, a is like a stall burning 2x 2m, shouting blind b is -5x 3 y 2, the result is -10x (2m+3)y 2—5x 3 y 2

Multiply the factors in parentheses separately.