Question

Find P, Q, R and S respectively.

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Equilateral Triangle	P
Rectangle		Q
Square	R		S

A.Intersection point of medians, 2, Intersection point of diagonals, \[90^\circ \]
B.Intersection point of medians, 2, Intersection point of diagonals, \[180^\circ \]
C.Intersection point of altitudes, 4, Intersection point of diagonals, \[25^\circ \]
D.Intersection point of sides, 4, Intersection point of diagonals, \[45^\circ \]

Answer 1

Hint: Here, we have to find the centre of rotation of equilateral triangle and square, order of rotation of the rectangle and angle of rotation of square. An equilateral triangle is a triangle in which all three sides have the same length. A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. A rectangle is a quadrilateral with four right angles.

Complete step-by-step answer:
We know that in an equilateral triangle the center lies at the point of intersection of medians, which gives the centre of rotation.
So, the centre of rotation of an equilateral triangle (P) is the intersection point of medians.
Now, we know a rectangle has order of rotation 2 because at \[180^\circ \] it will look the same and after rotating \[360^\circ \], it will again look the same as the rectangle.
So, we have an Order of Rotation of a rectangle (Q) is 2.
In square, the centre of rotation is given by the intersection point of the diagonal because the diagonal of the square bisects each other at \[90^\circ \] degree.
So, the center of rotation of square (R) is the intersection point of diagonals.
As all sides of the square are equal, so after rotating by \[90^\circ \] it will look the same as a square, so, the angle of Rotation (S) as \[90^\circ \].
From the above explanation we can conclude that P is the intersection point of medians, Q is 2, R is intersection point of diagonals and S is \[90^\circ \].
Hence, option A is the correct option.

Note: We know that the center of rotation is a point about which a plane figure rotates. This point does not move during the rotation. The number of positions in which a figure can be rotated and still appears exactly as it did before the rotation, is called the order of rotation. The angle through which the plane figure is rotated is called the angle of rotation.