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

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) (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=
d=
d=
d=
d= 5
l(BC)
x1 y1 x2 y2

4 0 1 4
d=
d=
d=
d=
d= 5

l(CD)
x1 y1 x2 y2

4 0 0 -3
d=
d=
d=
d=
d= 5
l(DA)
x1 y1 x2 y2

-3 1 0 -3
d=
d=
d=
d=
d= 5
The lengths are all 5 units. and they are at right angles. so it is a square.

RELATED QUESTIONS
Let f be the function defined by f(x)=(cx-(5x^2))/((2x^2)+ax+b), where a, b, and c are... (answered by solver91311)

According to this relation the value of Y when X = 5 is? Then teacher gives a table X= 0, (answered by rothauserc)

4) For the function, y=1/x-1 a) Give the y values for x = -1, 0, 1, 2, 3, 4 Answer: (answered by jim_thompson5910)

4) For the function, y=1 / x-1 a) Give the y values for x = -2, -1, 0, 1, 2, 3... (answered by rmromero)

4) For the function, y= 1 / x-1 a) Give the y values for x = -2, -1, 0, 1, 2, 3... (answered by rmromero)

A. Solve the following quadratic equations. Make sure to show all your work. Do not use... (answered by checkley71)

4) For the function, y=1/x-2 a) (answered by stanbon)

4) For the function, a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer:... (answered by stanbon)

For the function, a) Give the y values for x = -1, 0, 1, 2, 3, 4. Answer: Show (answered by stanbon)