SOLUTION: are these vertices of a square A(-3,1)B(1,4)C(4,0) D(0,-3) JUSTIFY ANSWER AND SHOW WORK THANK YOU

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Question 672501: are these vertices of a square A(-3,1)B(1,4)C(4,0) D(0,-3) JUSTIFY ANSWER AND SHOW WORK THANK YOU
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
A(-3,1)B(1,4)C(4,0) D(0,-3)
Find the slopes of AB,BC,CD,DA
Slope of AB
x1 y1 x2 y2
-3 1 1 4

slope m = (y2-y1)/(x2-x1)
( 4 - 1 )/( 1 - -3 )
( 3 / 4 )
m(AB)= 3/4
M(BC)
x1 y1 x2 y2
4 0 1 4

slope m = (y2-y1)/(x2-x1)
( 4 - 0 )/( 1 - 4 )
( 4 / -3 )
m= -4/3
m(CA)
x1 y1 x2 y2
4 0 0 -3

slope m = (y2-y1)/(x2-x1)
( -3 - 0 )/( 0 - 4 )
( -3 / -4 )
m= 3/4
m(AD)
x1 y1 x2 y2
-3 1 0 -3

slope m = (y2-y1)/(x2-x1)
( -3 - 1 )/( 0 - -3 )
( -4 / 3 )
m= -4/3

Two lines are having same slopes and two are having slopes negative reciprocal
So the angles formed are 90 degrees.
If the distances aer equal then the co ordinates form a square.
l(AB)
x1 y1 x2 y2

-3 1 1 4
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28%09%094%09-%091%09%29%5E2%09%2B%09%28%091%09-%09-3%09%29%5E2%09%29
d= sqrt%28%28%09%093%09%29%5E2%09%2B%09%28%094%09%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5
l(BC)
x1 y1 x2 y2

4 0 1 4
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%284-0%29%5E2%09%2B%281-4%29%5E2%29
d= sqrt%28%284%29%5E2%09%2B%28-3%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5

l(CD)
x1 y1 x2 y2

4 0 0 -3
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28-3-0%29%5E2%2B%280-4%29%5E2%29
d= sqrt%28%28-3%29%5E2%09%2B%28-4%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5
l(DA)
x1 y1 x2 y2

-3 1 0 -3
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
d= sqrt%28%28%09%09-3%09-%091%09%29%5E2%09%2B%09%28%090%09-%09-3%09%29%5E2%09%29
d= sqrt%28%28%09%09-4%09%29%5E2%09%2B%09%28%093%09%29%5E2%09%29
d= sqrt%28%28%09%0925%09%29++%09%29
d= 5
The lengths are all 5 units. and they are at right angles. so it is a square.