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As shown in the figure, in the plane rectangular coordinate system xoy, the vertex e coordinates of rectangular oefg are (4,0), and the vertex g coordinates are (0,2). Rotate the rectangular oefg anticlockwise around point O, so that point F falls on the point n of the Y axis, and the rectangle omnp, OM and GF intersect at point a (1) Judge whether △ OGA and △ NPO are similar and explain the reasons; (2) The analytic formula of inverse proportional function of point a is obtained; (3) If the image of the inverse scaling function obtained in (2) intersects with EF at point B, please explore whether the line AB is perpendicular to OM and explain the reason
(1) The reason is as follows: ∵ rotate the rectangle oefg anticlockwise around point o so that the point F falls on the point n of the y-axis, so that the rectangle omnp, ∵ P = ∽ ago = 90 °, PN ∥ OM, ∵ PNO = ∽ AOG, ∵ OGA ∵ NPO; (2) ∵ OGA ∽ NPO, ∵ OP = og = 2, PN = om = o
As shown in the figure, in the plane rectangular coordinate system, the vertex a of the parallelogram oabc is on the X axis, and the coordinates of the vertex B are (6,4). If the line L changes the parallelogram OAB As shown in the figure, in the plane rectangular coordinate system, the vertex a of the parallelogram oabc is on the X axis, and the coordinates of the vertex B are (6,4). If the straight line passes through the point (1,0), and the parallelogram oabc is divided into two parts with equal area, the function analytic formula of the line L is obtained
∵ the coordinates of point B are (6,4),
The central coordinates of the parallelogram are (3,2),
Let the function analytic formula of the line l be y = KX + B,
be
3k+b=2
k+b=0
The solution
K=1
B = - 1, so the analytic formula of the line L is y = X-1
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 plane rectangular coordinate system, the coordinates of vertices a and C of ▱ oabc are a (2,0) and C (- 1,2), respectively, and the inverse scale function y = K The image of X (K ≠ 0) passes through point B (1) Find the value of K (2) Turning ▱ oabc along the x-axis, the point C falls at the point C ', to judge whether the point C' is in the inverse proportional function y = K X (K ≠ 0), please explain the reason by calculation
(1) ∵ a quadrilateral oabc is a parallelogram, ? a (2,0), ? OA = 2, ? BC = 2, ? C (- 1,2), ? CD = 1, ᙽ BD = bc-cd = 2-1 = 1, ? B (1,2), ∵ the image of the inverse scale function y = KX (k ≠ 0) passes through point B, ? k = 1 × 2 = 2; (2) ? oabc folds along the x-axis, point C
As shown in the figure, in the plane rectangular coordinate system, the coordinates of the vertices a and C of the parallelogram oabc are a [2,0], C, [- 1,2], and the image of the inverse scale function y = K / x [K ≠ 0] passes through point B Q: find a point m on the y-axis. When the difference between line am and line cm reaches the maximum, find the point m coordinates that meet the conditions Explanation of strip graph
Make point C symmetric point d [1.2] with respect to y axis, and extend the connection ad to an intersection point with y axis, which is m point
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 (3,5) in the direction of mountain a → B with x unit length per second along the positive direction of Y axis to point B (3,5). When x and Y meet the above requirements, √ x + 2y-5 + (2x-y) 2 = 0, e, f move for 1 second, then find the coordinates of point E and F
∵√x+2y-5+(2x-y)²=0,
∴x+2y-5=0 2x-y=0
∴x=1 y=2
when exercise for 1 second, e (0,1), f (3,2)
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 (1) Write the coordinates of point B (,) (2) If the straight line CD passing through point C intersects the rectangle edge at point D, and the perimeter of the rectangle oabc is divided into two parts: 3:2, the coordinates of point D are calculated
1. Coordinates of point B (3,5)
2. (x + 3 + 5) / (3 + 5-x) = 3 / 2, x = 1.6, so the coordinate of D is (1.6,3)
If (X-2) 2 = 1 and x2-2mx + 1 = 0 have the same root, then M=______ .
From (X-2) 2 = 1
x-2=±1，
The solution is x = 3 or x = 1
When x = 3, 32-2 × 3M + 1 = 0, M = 5
3．
When x = 1, 12-2m + 1 = 0, M = 1
To sum up, M = 5
3 or M = 1
So the answer is: 5
3 or 1
It is known that a and B are two of the equations 2x? 2 + 14x-5 = 0, Find 1) (a + 1 / b) (B + 1 / a) 2) a 2 + 3AB + B? 3) a / B + B / a
Weida theorem: a + B = - 7 AB = - 5 / 2
1) (a+1/b)(b+1/a)=(ab+1)^2/ab=(-3/2)^2/(-5/2)=-9/10
2) a^2+3ab+b^2=(a+b)^2+ab=49-5/2=93/2
3) a/b+b/a=(a^2+b^2)/ab=[(a+b)^2-2ab]/ab=(49+5)/(-5/2)=-108/5
Given that X1 and X2 are two real roots of the equation 2x2 + 14x-16 = 0, then x2 x1+x1 The value of X2 is______ .
∵ X1 and X2 are the two real roots of the equation 2x2 + 14x-16 = 0,
According to Weida's theorem, X1 + x2 = - 7, x1 · x2 = - 8,
∴x2
x1+x1
x2=72−2×(−8)
−8=-65
8．
So the answer is: - 65
8．
RELATED INFORMATIONS
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