In the plane rectangular coordinate system, the points a (- 4,0) and B (2,0) are known. If the point C is in the first order function y = - 1 On the image of 2x + 2, and △ ABC is a right triangle, then the point C satisfying the condition has () A. 1 B. 2 C. Three D. Four

In the plane rectangular coordinate system, the points a (- 4,0) and B (2,0) are known. If the point C is in the first order function y = - 1 On the image of 2x + 2, and △ ABC is a right triangle, then the point C satisfying the condition has () A. 1 B. 2 C. Three D. Four

The intersection point of the line y = - 12x + 2 and the X axis is (4,0), and the intersection point with the Y axis is (0,2). As shown in the figure: point a is the intersection point of the vertical line and the straight line w (- 4,4), passing through point B is the intersection point s (2,1) of the vertical line and the straight line, and the intersection point of the vertical line and the straight line is f (- 1, 2.5)

As shown in the figure, in the plane rectangular coordinate system, O is the origin, the quadrilateral oabc is the rectangle, a (10, 0), C (0, 3), point D is the midpoint of OA, and point P moves on the edge of BC. When △ ODP is an isosceles triangle with waist length of 5, the coordinate of point P is______ .

Od = 5
∵ △ ODP is an isosceles triangle with waist length of 5
ν OP = 5 or PD = 5
Make od vertical line through P and intersect with OD at point Q
∴PQ=OC=3
If OP = 5, then OQ = 4, then the coordinates of point P are (4, 3);
If PD = 5, then QD = 4, OQ = 1, then the coordinates of point P are (1, 3);
If PD = 5, then QD = 4, OD = 5, OQ = 9, then the coordinates of point P are (9, 3)

Known, as shown in the figure: in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is the rectangle, and the coordinates of points a, C and D are (9,0)

As shown in the figure, in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is a rectangle, the coordinates of points a and C are a (10,0], C (0,4), M is the midpoint of OA, and point P moves on the edge of BC. (1) when Po = PM, the coordinates of point p; (2) when △ OPM is an isosceles triangle with waist length of 5, find the coordinates of point P. (1)

As shown in the figure: in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is a rectangle, and the coordinates of points a and C are a (10,0) and C (0,3), respectively Point D is the midpoint of OA, and point P moves on the edge of BC The third question on page 134 of the second grade of junior high school

（1,3）

It is known, as shown in the figure: in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is a rectangle, the coordinates of points a and C are a (10, 0), C (0, 4), respectively; point D is the midpoint of OA, and point P moves on the edge of BC; when △ ODP is an isosceles triangle with waist length of 5, the coordinates of point P are______ .

(1) When od is the bottom of an isosceles triangle, P is the intersection of the vertical bisector of OD and CB, and op = PD ≠ 5;
(2) When od is one waist of isosceles triangle:
① If point O is the vertex of the vertex angle, point P is the intersection point of the arc with point o as the center of the circle and radius of 5 with CB,
In right angle △ OPC, CP=
OP2-OC2=
If 52-42 = 3, then the coordinates of P are (3, 4)
② If D is the vertex of the vertex angle, point P is the intersection point of the arc with point D as the center of the circle and radius of 5 with CB,
D as DM ⊥ BC at point M,
In right angle △ PDM, PM=
PD2-DM2=3，
When p is on the left of M, CP = 5-3 = 2, then the coordinates of P are (2,4);
When p is on the right side of M, CP = 5 + 3 = 8, then the coordinates of P are (8, 4)
So the coordinates of P are: (3,4) or (2,4) or (8,4)
So the answer is: (3,4) or (2,4) or (8,4)

As shown in the figure, in the plane rectangular coordinate system, the vertex coordinates of rectangular oabc are (15,6), and the straight line y = 1x + B exactly divides the area of rectangular oabc into equal parts As shown in the figure, in the plane rectangular coordinate system, the vertex coordinates of rectangular oabc are (15,6), The straight line y = 1 / 3x + B just divides the area of rectangular oabc into two equal parts, and calculates the value of B;

Let the coordinates of B be (15,6), (because there is no graph, it is not clear that it is point B)
Then the intersection point with BD (3.5, AC)
∵ the straight line y = 1 / 3x + B exactly divides the area of the rectangular oabc into two equal parts
The line passes through the point (7.5,3)
∴3=1/3*7.5+b
3=2.5+b
b=1/2

As shown in the figure, in the plane rectangular coordinate system xoy, the vertex f coordinate of rectangular oefg is (4,2) As shown in the figure, in the plane rectangular coordinate system, the vertex f coordinates of rectangular oefg are (4,2). Rotate the rectangular oefg anticlockwise around point o so that point F falls on the Y axis, and the rectangle omnp, OM and GF intersect point A. if the image passing through the inverse scale function y = K / X (x > 0) of point a intersects EF at point B, the coordinates of point B are obtained

∵∠M=∠PGA=90°,∠MON=∠AOG,
∴ΔOGA∽ΔOMN,
∴GA/MN=OG/OM,
GA/2=2/4,
GA=1,
∴A(1,2),
Y = K / X over a (1,2),
The hyperbolic analytic formula y = 2 / x,
When x = 4, y = 1 / 2,
∴B(4,1/2).

As shown in the figure, in the plane rectangular coordinate system, the vertex a of ▱ oabc is on the x-axis, and the coordinates of vertex B are (6,4). If the straight line L passes through point (1,0) and ▱ oabc is divided into two parts with equal area, the function analytic formula of line L is () A. y=x+1 B. y＝1 3x+1 C. y=3x-3 D. y=x-1

Let D (1,0),
∵ line L passes through point d (1,0), and ▱ oabc is divided into two parts with equal area,
∴OD=BE=1，
∵ the coordinates of vertex B are (6, 4)
∴E（5，4）
Let the function analytic formula of the line l be y = KX + B,
∵ the image passes through D (1, 0), e (5, 4),
Qi
k+b＝0
5k+b＝4 ，
The solution is as follows:
k＝1
b＝−1 ，
The analytic formula of the function of the line L is y = X-1
Therefore, D

As shown in the figure, in the rectangular oabc, O is the origin of the plane rectangular coordinate system, the coordinates of points a and C are (3,0), (0,5), and point B is in the first quadrant. Point E is from point o Starting from point a, point F moves from point a to point B in the direction of y-axis with x unit length per second to point C. when the coordinates of point B and E are (0,1) f (3,2), and how long does point EF move, the straight line EF divides the area of rectangular oabc into 2:1 and calculates the coordinates of EF sit back and wait

（1）（3,5）
(2) if point D is on the straight line AB, the coordinates of point d (3, y) may be set
According to the meaning of the title, 0 ＜ y ＜ 5
∵ CD divides the circumference of rectangular oabc into 1:3 parts
∴(CB+BD):(OC+OA+AD)=1:3
That is (3 + 5-y): (3 + 5 + y) = 1:3
The solution is y = 4
So the coordinates of point d (3,4)
(3) if the line CD in (2) is shifted downward by 2 units, then c '(0,3), d' (3,2)
Then ad '= 2, OC' = 3, OA = 3
It can be seen from the figure that the quad oad ` C 'is a right angled trapezoid
The area of the quad oad ` C '= (ad' + OC ') OA / 2
=(2+3)×3÷2
=7.5

As shown in the figure, in rectangular oabc, O is the origin of plane rectangular coordinate system, the coordinates of points a and C are (3,0), (0,5), and point B is in the first quadrant As shown in the figure, in rectangular oabc, O is the origin of plane rectangular coordinate system, the coordinates of points a and C are (3,0), (0,5), and point B is in the first quadrant (1) Write the coordinates of point B; (2) (2) if the straight line CD passing through point C intersects AB at point D, and the circumference of the rectangular oabc is divided into two parts, i.e. 5:3 (3) Translate the segment CD in (2) to obtain C'd ', so that C'd' bisects the area of rectangular oabc, then the coordinates of point d 'are————

B(3,5)
D(3,2)
D '(3,2-radical 2 / 2)