Question

If P(-4, k), Q(k, 5), R(2, k), S(k, 5) are the coordinates of a rectangle, find the value of k. Also find the coordinates​

Answer 1

Answer

Let the three points be P(0,2), A(3, K) and B(k,5).

and, AP=BP

⇒AP

2

=BP

2

⇒(3−0)

2

+(k−2)

2

=(k−0)

2

+(5−2)

2

⇒9+k+4−4k=k

2

+9

⇒4k=4

⇒k=1