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Question

The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) form a ___


A

Square

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B

Rectangle

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C

Parallelogram

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D

Rhombus

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Solution

The correct option is B

Rectangle


We know that, distance between the points (x1,y1) and (y2,y2)
d=(x2x1)2+(x2y1)2

So, distance between A(-1,-2) and B(4, 3)
AB=(4+1)2+(3+2)2=52+52=25+25=52

Distance between C(2,5) and D(-3,0)
CD=(32)2+(05)2=(5)2+(5)2=25+25=52

Distance between A(-1,-2) and D(-3,0),
AD=(3+1)2+(0+2)2=(2)+22=4+4=22
Similarly, BC = 22
We know that, in a rectangle, opposite sides are equal and diagonals are equal and they bisect each other.
Since, AB = CD and AD = BC

Distance between A(-1,-2) and C(2,5)
AC=(2+1)2+(5+2)2=32+72=9+49=58

And distance between D(-3,0) and B(4,3),
DB=(4+3)2+(30)2=72+32=49+9=58

Since, the diagonals AC and BD are equal.
the points A(-1,-2), B(4,3), C(2,5) and D(-3,0) form a rectangle.



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