Determine whether AB is parallel to CD.
Problem 1 :
A(5, 6), B(-1, 3), C(-4, 9), D(-16, 3)
Solution:
Slope of AB:
A(5, 6) ==>(x_{1}, y_{1}), B(-1, 3) ==> (x_{2}, y_{2})
Slope of CD:
C(-4, 9) ==>(x_{1}, y_{1}), D(-16, 3) ==> (x_{2}, y_{2})
Slope of AB = Slope of CD
1/2 = 1/2
So, slope of the lines AB and CD are equal.
Hence, the line AB is parallel to CD.
Problem 2 :
A(-3, 6), B(5, 4), C(-14, -10), D(-2, -7)
Solution:
Slope of AB:
A(-3, 6) ==>(x_{1}, y_{1}), B(5, 4) ==> (x_{2}, y_{2})
Slope of CD:
C(-14, -10) ==>(x_{1}, y_{1}), D(-2, -7) ==> (x_{2}, y_{2})
Slope of AB ≠ Slope of CD
-1/4 ≠ 1/4
So, the lines are neither parallel nor perpendicular.
Problem 3 :
A(6, -3), B(5, 2), C(-4, -4), D(-5, 2)
Solution:
Slope of AB:
A(6, -3) ==>(x_{1}, y_{1}), B(5, 2) ==> (x_{2}, y_{2})
Slope of CD:
C(-4, -4) ==>(x_{1}, y_{1}), D(-5, 2) ==> (x_{2}, y_{2})
Slope of AB ≠ Slope of CD
-5 ≠ -6
So, the lines are neither parallel nor perpendicular.
Problem 4 :
A(-5, 6), B(-7, 2), C(7, 1), D(4, -5)
Solution:
Slope of AB:
A(-5, 6) ==>(x_{1}, y_{1}), B(-7, 2) ==> (x_{2}, y_{2})
Slope of CD:
C(7, 1) ==>(x_{1}, y_{1}), D(4, -5) ==> (x_{2}, y_{2})
Slope of AB = Slope of CD
2 = 2
So, slope of the lines AB and CD are equal.
Hence, the line AB is parallel to CD.
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