Question

A rectangle is drawn with its centre (5, 4) whose width and height are 10 and 8 respectively. Of the rectangle is rotated 45 around its centre in clockwise direction what is the new location of the corner which is closest to the centre

Answer 1

Answer:

See the explanation.

Step-by-step explanation:

The width and height of the given rectangle is 10 and 8.

The length of the diagonals is $\sqrt{(10^{2} ) + 8^{2} } = \sqrt{164}$.

The diagonals of any rectangle divide them in equal length.

Hence, the distance between the vertices and the center (5, 4) is  $\frac{\sqrt{164} }{2} = \sqrt{41}$.

It is not given that the rectangle's sides are parallel with the axis-es or not.

Hence, the exact location of vertices can not be determined as the vertices can be situated on any point on the circle of radius $\sqrt{41}$ centered at (5, 4).

If one of the particular vertex can be determined, then the new location could also be determined by rotating the joining line of (5, 4) and the vertex through 45 degree in a clockwise direction.