Question

Three vertices of a rectangle are given. Find the coordinates of the fourth vertex.

(2, 5), (6, 1), (4, –1)

A.
(0, 2)

B.
(0, 3)

C.
(1, 3)

D.
(1, 4)

Answer 1

The distance between (2,5) and (6,1) is:


`\sf Distance = √(\left( 6 - 2 \right)^2 + \left( 1 - 5 \right)^2) \\\\ =√( 16 + 16) \\ \\ = \boxed{\bf{4 √( 2 ) }}`

The distance between the fourth vertex and (4,-1) should also be 4√2

The only point that gives us that distance is B. (0,3)


`\sf Distance = √(\left( 4 - 0 \right)^2 + \left( -1 - 3 \right)^2) \\ \\= √( 16 + 16) \\ \\ = \boxed{\bf{4 √( 2 ) }}`

Your final answer is B. (0,3)