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In the plane Cartesian coordinate system, if the line y = 3x-2 is transformed axisymmetrically about the X axis, and then the obtained line is transformed axisymmetrically about the Y axis, then the expression of the obtained line after two transformations is () A. y=2x-3B. y=3x-2C. y=2x+3D. y=3x+2
∵ the abscissa of the point with X-axis symmetry is invariable, and the ordinates are opposite to each other, ∵ the analytical formula of the line obtained by axisymmetric transformation of the line y = 3x-2 with respect to x-axis is: - y = 3x-2; ∵ the ordinate of the point with Y-axis symmetry is invariable, and the abscissa is opposite to each other, ∵ the analytical formula of the line obtained by axisymmetric transformation of the line y = 3x-2 with respect to x-axis is: - y = - 3x-2, that is y = 3x + 2 Choose D
（1）（y^3）^2+（y^2）^3-2y*y^5 （2）（3x+2)（3x-2)-5x（x-1)-（2x-1)（2x-1)
（1）（y^3）^2+（y^2）^3-2y*y^5
=y^6+y^6-2y^6
=0
（2）（3x+2)（3x-2)-5x（x-1)-（2x-1)（2x-1)
=9x²-4-5x²+5x-(4x²-4x+1)
=4x-5
If point P (3x-1,4 + 5Y) and point Q (5 + X, 2y-2) are symmetric about the Y axis, find the values of X and y
On Y-axis symmetry
be
The abscissa values are opposite to each other
3x-1+5+x=0
4x=-4
x=-1
The ordinate values are equal
4+5y=2y-2
3y=-6
y=-2
Solution
x=-1
y=-2
Given that point P (2x-1,3x) and point B (x, y) are symmetric about X axis, find the value of X, y
Because point P (2x-1,3x) and point B (x, y) are symmetric about the X axis
So 2x-1 = x, x = 1
3x=-y y=-3
Point a (3x-2, Y-5) and B (2Y + 3, - x + 4) are symmetric with respect to x = 2. Find the coordinates of P (x, y) with respect to the y-axis symmetric point Q
On x = 2 symmetry
So (3x-2 + 2Y + 3) / 2 = 2
y-5=-x+4
Namely
3x+2y=3
x+y=9
So x = - 15
y=24
P(-15,24)
So Q (15,24)
Given that P1 (a-2,4) and P2 (2, B-1) are symmetric about X axis, the values of a and B are obtained
Be easy to understand and clear
Because P1 and P2 are symmetric with respect to family x, a ― 2 = negative 2, B ― 1 = negative 4, so a = 0, B = negative 3
If P is a symmetric point P1 (2m + N, - M + 1) about X axis and P2 (4-N, N + 2) about y axis, then the coordinate of P is ()
If P is symmetric point P1 (2m + N, - M + 1) about X axis and P2 (4-N, N + 2) about y axis, then the coordinates of P point are () P, symmetric point p1p about X axis, symmetric point P2 about y axis, and P2 about origin
(1) As shown in the figure, ∠ mon = 80 °, points a and B move on ray OM and on respectively, and the angular bisector AC and BD of △ AOB intersect at point P
Will the size of ∠ APB change with the change of setting? If it remains unchanged, ask for the degree of ∠ APB. If it changes, find out the range of change
(2) Draw two intersecting straight lines ox and oy so that ∠ xoy = 60 °, ② take any two points a and B on the ray ox and oy respectively, ③ make the bisector BD of ∠ aby, and the reverse extension of BD intersects the bisector of ∠ OAB at point C. with the change of the position of points a and B, will the size of ∠ C change? If it remains unchanged, ask for the degree of ∠ C. if it changes, find out the range of change
(1) It doesn't change ∠ APB = 180 - ∠ ABP - ∠ BAP = 180-1 / 2 ‰ abo-1 / 2 ‰ Bao = 180-1 / 2 (180 - ∠ AOB) = 180-1 / 2 * 100 = 130 (2) ∠ C = 180 - ∠ Cab - ∠ ABC = 180-1 / 2 ‰ OAB - (180-1 / 2 ‰ aby) = 180-1 / 2 ‰ oab-180 + 1 / 2 ‰ aby = 1 / 2 (∠ aby - ∠ OAB) = 1 / 2 (180 - ∠ oba - ∠ o)
A very simple problem! As shown in the figure, P is any point in ∠ AOB. Take OA and ob as the axis of symmetry, draw the points P1 and P2 of P after the change of axis symmetry, and connect P1 and P2
If P1, P2 = 8cm, calculate the perimeter of △ PCD
You master answer! ~ ~ ~ thank you! Good absolutely can add points! A very simple question!
Please draw the picture by yourself. Sorry! If there are conditions, in the "Meng Jianping" seven mathematics series can be found! O(∩_ Thank you! Please write down the process of solving the problem, add higher!!! ~~~~~~~~~~~~~~
P1D = DP, PC = CP2 (symmetrical)
The perimeter of PCD = DP + PC + CD = P1D + DC + CP2 = p1p2 = 8cm
As shown in the figure, ∠ mon = 90 ° points a and B move on ray OM and on respectively,
The bisector of the angle OAB and the straight line of the outer corner line of the angle oba intersect at point C. when the angle AOB = 90 degrees, does the size of the angle ACB change as a and B move to OA not equal to ob
The size of C remains unchanged
∵∠ ABN = 90 ° + ∠ OAB, AC bisection ∠ OAB, BD bisection ∠ ABN,
∴∠ABD=12∠ABN=12（90°+∠OAB）=45°+12∠OAB,
That is ∠ abd = 45 °+ ∠ cab,
And ∵ ∠ abd = ∠ C + ∠ cab,
∴∠C=45°,
Therefore, the size of ∠ ACB does not change, and it always keeps 45 degrees
RELATED INFORMATIONS
- 1. Known: as shown in the figure, ∠ mon = 90 °, points a and B move on ray OM and on respectively, AC bisects ∠ OAB, BD bisects ∠ ABN, AC and DB intersect at point C. try to guess: as points a and B move, does the size of ∠ ACB change? Prove your conclusion
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- 19. In the plane rectangular coordinate system, point a (0,3), point B (3,1) and point P are on the x-axis, and the minimum value of PA + Pb is obtained?
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