Maths / Coordinate Geometry / Distance Formula

QUESTION

Name the type of quadrilateral formed by the points (1, 7), (4, 2), (-1,-1) and (-4, 4).

EXPLANATION
Explain TypeExplanation Content
Text

Let the points be  A=(1, 7), B=(4, 2), C=(-1,-1) and  D=(-4, 4).

$\large \large AB = \sqrt{(4-1)^2+(2-7)^2} =\sqrt{9+25} =\sqrt{34}$

$\large \large BC = \sqrt{(-1-4)^2+(-1-2)^2} =\sqrt{25+9} =\sqrt{34}$

$\large \large CD = \sqrt{(-4-(-1))^2+(4-(-1))^2} =\sqrt{9+25} =\sqrt{34}$

$\large \large DA = \sqrt{(-4-1)^2+(4-7)^2} =\sqrt{25+9} =\sqrt{34}$

$\large \large AC = \sqrt{(-1-1)^2+(-1-7)^2} =\sqrt{4+64} =\sqrt{68}$

$\large \large BD = \sqrt{(-4-4)^2+(4-2)^2} =\sqrt{64+4} =\sqrt{68}$

As all the sides are equal so the quadrilateral can be square or a rhombus but as the diagonals are equal therefore it is a square

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