Fewpal
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ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.

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by (25.4k points)
 
Best answer

Solution: Coordinates of P can be calculated as follows:

10 coordinate exercise solution

Coordinates of Q can be calculated as follows:

10 coordinate exercise solution

Coordinates of R can be calculated as follows:

10 coordinate exercise solution

Coordinates of S can be calculated as follows:

10 coordinate exercise solution

Length of PQ can be calculated as follows:

10 coordinate exercise solution

Similarly, QR can be calculated as follows:

10 coordinate exercise solution

The above values show that RS = PS, i.e. all sides are equal.

Now let us calculate the diagonals

10 coordinate exercise solution

Hence, it is clear that while all sides are equal, diagonals are not equal. So, the given figure is a rhombus.

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