Answered

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)

Verified Answer :

Leader

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

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

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)

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

Your final answer is B. (0,3)

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