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Question

What type of a quadrilateral do the points A(2,2),B(7,3),C(11,1) and D(6,6) taken in that order, form?

A
Scalene quadrilateral
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B
Square
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C
Rectangle
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D
Rhombus
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Solution

The correct option is A Scalene quadrilateral
Given that the point
A(x1,y1)=(2,2),B(x2,y2)=(7,3),C(x3,y3)=(11,1) and D(x4,y4)=(6,6) form a quadrilateral ABCD.
Its type will be (i) a scalene one, if AC≠BD, (ii) a rectangle, if AC=BD.
We apply the distance formula, to get
d=√(x2−x1)2+(y2−y1)2
∴AC=√(x3−x1)2+(y3−y1)2=√(11−2)2+(1−2)2 units
=√82units and
BD=√(x4−x2)2+(y4−y2)2=√(6−7)2+(3−6)2 units
=√10 units
So, AC≠BD
∴ABCD is a scalene quadrilateral.
Also,
AB=√(7−2)2+(3−2)2=√26 units
BC=√(11−7)2+(1−3)2=√20 units
Thus, the sides are not equal. So, they does not represent a rhombus or a square.
Hence, only option A is correct.

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