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On which axis do the following points lie?
(i) 
P(5,0)
(ii) 
Q(0-2)
(iii) 
R(-4,0)
(iv) 
S(0,5)
Let 
ABCD be a square of side 
2a. Find the coordinates of the vertices of this square when
(i) A coincides with the origin and 
AB and 
AD are along 
OX and 
OY respectively.
(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides 
AB and 
AD respectively,
BASED ON LOTS

11. On which axis do the following points lie?\newline(i) P(5,0) P(5,0) \newline(ii) Q(02) \mathrm{Q}(0-2) \newline(iii) R(4,0) R(-4,0) \newline(iv) S(0,5) S(0,5) \newline22. Let ABCD A B C D be a square of side 2a 2 a . Find the coordinates of the vertices of this square when\newline(i) A coincides with the origin and AB A B and AD A D are along OX O X and OY O Y respectively.\newline(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides AB A B and AD A D respectively,\newlineBASED ON LOTS

Full solution

Q. 11. On which axis do the following points lie?\newline(i) P(5,0) P(5,0) \newline(ii) Q(02) \mathrm{Q}(0-2) \newline(iii) R(4,0) R(-4,0) \newline(iv) S(0,5) S(0,5) \newline22. Let ABCD A B C D be a square of side 2a 2 a . Find the coordinates of the vertices of this square when\newline(i) A coincides with the origin and AB A B and AD A D are along OX O X and OY O Y respectively.\newline(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides AB A B and AD A D respectively,\newlineBASED ON LOTS
  1. Points on x-axis: Points on the x-axis have a y-coordinate of 00, so P(5,0)P(5,0) and R(4,0)R(-4,0) lie on the x-axis.
  2. Points on y-axis: Points on the y-axis have an xx-coordinate of 00, so Q(0,2)Q(0,-2) and S(0,5)S(0,5) lie on the y-axis.
  3. Coordinates of square ABCD: For the square ABCD with side 2a2a, when A is at the origin and AB is along OX, the coordinates of A are (0,0)(0,0), B are (2a,0)(2a,0), D are (0,2a)(0,2a), and C are (2a,2a)(2a,2a).
  4. Coordinates of square center: For the square ABCDABCD with side 2a2a and center at the origin, the coordinates of AA are (a,a)(-a,-a), BB are (a,a)(a,-a), CC are (a,a)(a,a), and DD are (a,a)(-a,a).

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