As shown in the figure, the position of right angled trapezoid oabc in the plane rectangular coordinate system is as follows: ab ∥ OC, B (5,3), ab = BC. D (x, 0) is the moving point on OC (not coincident with O and C), DP ⊥ X axis intersects PC at point P, connecting Pb (1) The coordinates of point C are - (2) (1) as shown in figure (1), use the algebraic expression of X to represent the coordinates of point P, and find the value of X when △ PBC becomes a right triangle ② When point P is the intersection of trapezoidal diagonal AC and Bo (as shown in Figure 2), find the value of X

As shown in the figure, the position of right angled trapezoid oabc in the plane rectangular coordinate system is as follows: ab ∥ OC, B (5,3), ab = BC. D (x, 0) is the moving point on OC (not coincident with O and C), DP ⊥ X axis intersects PC at point P, connecting Pb (1) The coordinates of point C are - (2) (1) as shown in figure (1), use the algebraic expression of X to represent the coordinates of point P, and find the value of X when △ PBC becomes a right triangle ② When point P is the intersection of trapezoidal diagonal AC and Bo (as shown in Figure 2), find the value of X

fifty-six

As shown in the figure, in the square ABCD with side length of 4, the moving point P starts from point a and moves along AB to point B at the speed of 1 unit length per second, while the moving point Q starts from point B and moves along BC → CD at the speed of 2 unit lengths per second. When P moves to point B, P and Q stop moving at the same time. Let P move for T and the area of △ Apq be s, then the function relationship between S and t

Point P moves on AB, point Q moves on BC, point P moves on AB, point Q moves on CD, and the relation between S and t is obtained in turn. Point P moves on AB, point Q moves on BC, at this time AP = t, QB = 2T, so s = 1 / 2 apqb = t, and the function image is parabola. Point P moves on AB

As shown in the figure, in the plane rectangular coordinate system, a (1,1), B (- 1,1), C (- 1, - 2), D (1, - 2). Make a length of 2012 units

∵A（1,1）,B（-1,1）,C（-1,-2）,D（1,-2）,
∴AB=1-（-1）=2,BC=1-（-2）=3,CD=1-（-1）=2,DA=1-（-2）=3,
The length of the thin line around the quadrilateral ABCD is 2 + 3 + 2 + 3 = 10,
2012÷10=201… 2,
The other end of the thin wire is at the position of the second unit length around the 202 th circle of the quadrilateral,
That is, the position of point B, and the coordinates of the point are (- 1,1)
So choose B

If the point m (a, 2A + 1) is in the third quadrant, then the value range of a is

The third quadrant x < 0 y < 0
a＜0
2a+1＜0
a＜-1/2