Question

Which of the following points should be included with A(1,3) and B(3,7) so that the figure formed by connecting the points is a closed figure with the least number of sides?

• A. C(0,1)
• B. C(2,5)
• C. C(4,9)
• D. C(5,3)

Answer 1

The correct option is D C(5,3)

The closed figure with the least number of sides is a triangle. So, the figure formed by connecting the points A, B and C should be a triangle.

Plotting and connecting the points in each case, we find:

$Case1:A(1,3);B(3,7;C(0,1)$


$Case2:A(1,3);B(3,7);C(2,5)$


$Case3:A(1,3);B(3,7);C(4,9)$


$Case4:A(1,3);B(3,7);C(5,3)$


Hence, the only case where ABC is a triangle is in case 4.

Therefore, the coordinates of the third point will be C(5,3).