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In the rectangular coordinate system, the first order function y = x + m and the inverse proportional function y = m / X intersect point a in the first quadrant, intersect point C with X axis, AB is perpendicular to X axis, perpendicular foot is B, and the area of triangle ABO is 1
Let m + x = m + 2, and let m + x = m + 2 be the area of the triangle
As shown in the figure, in the parallelogram ABCD, de ⊥ AB is in E and DF ⊥ BC is in F. if the circumference of parallelogram ABCD is 48, de = 5, DF = 10, ① find the length of AB; ② find the area of parallelogram ABCD
① Let AB = x, then BC = 24-x. according to the area formula of parallelogram, we can get: 5x = 10 (24-x),
X = 16
AB = 16
②∵AB=16，DE=5，
The area of the parallelogram ABCD is 5 × 16 = 80
As shown in the figure, ▱ ABCD, de bisects AB vertically. The circumference of ABCD is 5cm, and the circumference of △ abd is 1.5cm less than that of ▱ ABCD. Find the length of each side of a parallelogram
Because de bisects AB vertically, Da = dB,
Let ad = x, ab = y,
2x+2y＝5
2x+y＝5−1.5 ，
The solution
x＝1
y＝1.5 ，
Therefore, the length of each side of a parallelogram is 1,1.5,1,1.5
As shown in the figure, in the parallelogram ABCD, BC = 4, ∠ ABC = 120 °, take the straight line where AB is located as the X axis and a as the origin to establish a plane rectangular coordinate system, and calculate the coordinates of four points a, B, C, D
A (0,0) B (4,0) C (6,2 ^ 3) d (2,2 ^ 3) ^ is the root sign
As shown in the figure, in the parallelogram ABCD, we know that ab = 4, BD = 3, ad = 5, and take the straight line where AB is located as the x-axis. Take point B as the origin to establish a plane rectangular coordinate system. Rotate the parallelogram ABCD anticlockwise around point B so that point C falls on the positive half axis of Y axis. The rotated positions of C, D and a are p, Q and t respectively (1) Verification: point D is on the Y axis; (2) If the line y = KX + B passes through two points P and Q, the analytic formula of line PQ is obtained
How can I find that there is something wrong with your question: 1, ab = 4, BD = 3, ad = 5, with point B as the origin of coordinates, then the condition you give is that ABC is a right triangle, and ab is the X axis, that is to say, the angle between AB and AC is 45 degrees, when you reverse
For a parallelogram, ABCD, ∠ a = 60 °, ab = 2, ad = 1, if the coordinate of point a is the origin, the angle between AB and the positive half axis of x-axis is 30 ° to find the coordinate of parallelogram
A (0,0); B (radical 3,1); C (radical 3,2); D (0,1). Because ∠ a = 60 ° ad = 1, AB is 30 ° to the positive half axis of X, so ad is perpendicular to the X axis. Then a (0,0) sets the vertical point of ab on the positive half axis of X as P, so AP = radical 3, Pb = 1, then B (radical 3,1). Then PC = Pb + BC = 1 + 1 = 2
As shown in the figure, in the plane rectangular coordinate system, each side of the rectangle ABCD is parallel to the x-axis and y-axis respectively. Its length ad is 6 and the width AB is 3. The coordinates of a are known to be (- 1,2), please write the coordinates of the other three vertices B, C and D of the rectangle
B is above a, C is above D
B(-1,5),C(5,5),D(5,2)
In the plane rectangular coordinate system, the coordinate of point a is (2,0), and point P is on the straight line y = - x + m, and AP = OP = 2?
Because OP = AP,
So p is on the vertical bisector of line OA,
The result shows that the height of OA of the base of OPA of isosceles triangle is √ 3,
There are two cases,
When p is in the first quadrant, P (1, √ 3)
If y = - x + m, M = √ 3 + 1 can be obtained
When p is in the fourth quadrant, P (1, √ 3)
If y = - x + m, M = - √ 3 + 1 can be obtained
In the plane rectangular coordinate system, the coordinate of point a is (4,0), the point P is on the straight line y = - x + m, and AP = OP = 4
Given AP = OP, point P is on the vertical bisector PM of line OA
∴OA=AP=OP=4，
The △ AOP is an equilateral triangle
As shown in the figure, when point P is in the first quadrant, OM = 2, Op = 4
In RT △ OPM, PM=
OP2-OM2=
42-22=2
3, (4 points)
∴P（2，2
3）．
∵ point P is on y=-x+m,
∴m=2+2
3. (6 points)
When the point P is in the fourth quadrant, according to the symmetry, P ′ (2, - 2)
3）．
∵ the point P ′ is on y = - x + M,
∴m=2-2
3. (8 points)
Then the value of M is 2 + 2
3 or 2-2
3．
In the plane rectangular coordinate system, the coordinate of point a is (4,0), the point P is on the straight line y = - x + m, and AP = OP = 4
Given AP = OP, point P is on the vertical bisector PM of line OA
∴OA=AP=OP=4，
The △ AOP is an equilateral triangle
As shown in the figure, when point P is in the first quadrant, OM = 2, Op = 4
In RT △ OPM, PM=
OP2-OM2=
42-22=2
3, (4 points)
∴P（2，2
3）．
∵ point P is on y=-x+m,
∴m=2+2
3. (6 points)
When the point P is in the fourth quadrant, according to the symmetry, P ′ (2, - 2)
3）．
∵ the point P ′ is on y = - x + M,
∴m=2-2
3. (8 points)
Then the value of M is 2 + 2
3 or 2-2
3．
RELATED INFORMATIONS
- 1. In the plane rectangular coordinate system, the coordinate of point a is (4,0), and the point P is on the straight line y = x-m, and AP = OP = 4
- 2. As shown in the figure, in the plane rectangular coordinate system, ⊙ P and X axis are tangent to origin o, and the straight line parallel to y axis intersects ⊙ P at M and N. if the coordinates of point m are (2, - 1), then the coordinates of point n are () A. （2，-4） B. （2，-4.5） C. （2，-5） D. （2，-5.5）
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