Question

Math 2 MYP | 2.2a Checking for understanding

5 For the points P(10, 13), Q(17, 37), R(24, 13), and S(17, -11):
a Find the distances PQ, QR, RS and SP.
b Robin says: 'the lengths PQ, QR, RS and SP are all equal, so the shape
PQRS must be a square.' Determine whether Robin is correct.
c Robin's logical process was:
Premises:
Reasoning process:
Conclusion:
The four lengths are equal.
If a quadrilateral has four equal sides, then it is a square.
Since PQRS has four equal sides, it is a square.
PQRS is a square.
Explain the fault in Robin's logic.

Answer 1

a To find the distances PQ, QR, RS, and SP, we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

The distances are:

PQ = √((17 - 10)^2 + (37 - 13)^2) = √(49 + 24) = √73 = 8.6
QR = √((24 - 17)^2 + (13 - 37)^2) = √(49 + 24) = √73 = 8.6
RS = √((17 - 24)^2 + (-11 - 13)^2) = √(49 + 144) = √193 = 13.9
SP = √((10 - 17)^2 + (13 - (-11))^2) = √(49 + 144) = √193 = 13.9

b No, the lengths PQ, QR, RS, and SP are not all equal. Therefore, the shape PQRS is not a square.

c The fault in Robin's logic is that the premise "if a quadrilateral has four equal sides, then it is a square" is not always true. A quadrilateral with four equal sides is known as a rhombus, not a square. A square is a special type of rhombus in which all four sides are equal in length and all four angles are right angles.