Find P,Q,R and S respectively

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Intersection point of medians, 2, Intersection point of diagonals, 90∘

Intersection point of medians, 2, Intersection point of diagonals, 180∘

Intersection point of altitudes, 4, Intersection point of diagonals, 25∘

Intersection point of sides, 4, Intersection point of diagonals, 45∘

answer is A.

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Detailed Solution

We know that in an equilateral triangle the center lies at the point of intersection of medians, which gives the center of rotation.
So, the center 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∘ it will look the same and after rotating 360∘, 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 center of rotation is given by the intersection point of the diagonal because the diagonal of the square bisects each other at 90∘ 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∘ it will look the same as a square, so, the angle of Rotation (S) as 90∘.
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∘.
Hence, option 1 is the correct option.

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