Question

What shape is obtained if the points A(5,6), B(1,5), C(2,1), and D(6,2) are joined in that order?

Answer 1

We find the 4 distances AB,BC,CD and DA.
AB=√(1-5)²+(5-6)²=√(16+1)=√17
BC=√(2-1)²+(1-5)²=√1+16=√17
CD=√(6-2)²+(2-1)²=√16+1=√17
DA=√(5-6)²+(6-2)²=√1+16=√17
Also, AC=√(2-5)²+(1-6)²=√9+25=√34
and, BD=√(6-1)²+(2-5)²=√25+9=√34
∵, All the sides are equal and both the diagonals are equal thus its a square.

Answer 2

AB=√(1-5)²+(5-6)²=√(16+1)=√17 BC=√(2-1)²+(1-5)²=√1+16=√17 CD=√(6-2)²+(2-1)²=√16+1=√17 DA=√(5-6)²+(6-2)²=√1+16=√17 Also, AC=√(2-5)²+(1-6)²=√9+25=√34 and, BD=√(6-1)²+(2-5)²=√25+9=√34 this is the answer