Question

Show that the points a (5,6) b(1,5) c (2,1) d (6,2) are verices of square?​

Answer 1

Answer:

Use distance formula to find the distance between a and b, then again between b and c, then c and d, and then d and a.

if all the distances are equal then it is a rhombus with all sides equal, else it is not a rhombus and hence it is not a square.

now, find the distance between the opposite points, that is between a and c and then between b and d.

this will give you the length of the two diagonals.

if both the lengths are equal then the rhombus is a square, else the rhombus is not a square.

i hope it helps.

Answer 2

Answer:

AB

$\sqrt{(1 - 5) {}^{2} + (5 - 6) {}^{2} } \\ \\ = \sqrt{16 + 1} = \sqrt{17} \: units$

BC $\sqrt{(2 + 1) {}^{2} + (1 - 5) {}^{2} } \\ \\ = \sqrt{1 + 16} \\ \\ = \sqrt{17} \: units$

CD = $\sqrt{(2 - 6) {}^{2} + (1 - 5) {}^{2} } \\ \\ = \sqrt{1 + 16} = \sqrt{17} \: units$

DA = $\sqrt{(6 - 5) {}^{2} + (2 - 6) {}^{2} } \\ \\ = \sqrt{1 + 16} \\ \\ = \sqrt{17} \: units$

AC =

$\sqrt{(2 - 5) {}^{2} + (1 - 6) {}^{2} } \\ \\ = \sqrt{9 + 25} \\ \\ = \sqrt{34} \: units$

BC $\sqrt{(6 + 1) {}^{2} + (2 - 5) {}^{2} } \\ \\ = \sqrt{(7) {}^{2} + ( - 3) {}^{2} } \\ \\ = \sqrt{34} \: units$

AB = BC = CD = DA = $\sqrt{17} \: units$

AC = BD = $\sqrt{34} \: units$

Thus, A, B, C and D are vertices of square.