Question

If three consecutive vertices of a rectangle are (2,3), (4, 6) and
(6, 7) then coordinates of the fourth vertex are
(2, 2)
(3,3)
(4,4)
(6, 6)​

Answer 1

Solution :-

Let the three consecutive vertices of a rectangle ABCD are A(2,3), B(4, 6) and C(6, 7) .

Let us assume that, coordinates of the fourth vertex is D(x, y) .

So,

→ Mid point of AC = (2 + 6)/2 and (3 + 7)/2 = (4, 5)

and,

→ Mid point of BD = (4 + x)/2 and (6 + y)/2

since,

→ Mid point of AC = Mid point of BD

→ (4,5) = (4 + x)/2 , (6 + y)/2

then,

→ (4 + x)/2 = 4

→ 4 + x = 8

→ x = 4

and,

→ (6 + y)/2 = 5

→ 6 + y = 10

→ y = 4

therefore, the coordinates of the fourth vertex are (4 , 4) .

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