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Question 12
The points A(-1, -2), B(4,3), C(2,5) and D(-3,0) in that order form a rectangle.


Solution

True
Distance between A(-1,-2) and B(4, 3)
AB=(4+1)2+(3+2)2=52+52=25+25=52Distance between C(2,5) and D(-3,0)CD=(32)2+(05)2=(5)2+(5)2=25+25=52

[distance between the points(x1,y1) and (y2,y2)d=(x2x1)2+(x2y1)2]Distance between A(-1,-2) and D(-3,0),AD=(3+1)2+(0+2)2=(2)+22=4+4=22
Distance between B(4,3) and C(2,5),BC=(24)2+(53)2=(2)+22=4+4=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
Also, 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, diagonals AC and BD are equal.

Hence, the points A(-1,-2), B(4,3), C(2,5) and D(-3,0) form a rectangle.

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