Question 614017: The coordinate points of a parallelogram are A(-3,-1) B(-1,7) C(2,2) D(0,-6).
(a) What is slope of segment CD? A.) 8/2 B.) -2/8
(b) What is the slope of any segment that would be perpendicular to segment CD?
(c) Use the slope determined in the previous problem to draw a height for the parallelogram from point A to segment CD. Label the point where the height intersects segment CD as point E. What are the coordinates of point E?
A.) 8/2 B.) -2/8
I really need help figuring out how to find these coordinates!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The coordinate points of a parallelogram are A(-3,-1) B(-1,7) C(2,2) D(0,-6).
(a) What is slope of segment CD?
slope = (-6-2)/(0-2) = -8/-2 = 4
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(b) What is the slope of any segment that would be perpendicular to segment CD?
Ans: -1/4
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(c) Use the slope determined in the previous problem to draw a height for the parallelogram from point A to segment CD. Label the point where the height intersects segment CD as point E. What are the coordinates of point E?
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A(-3,-1) slope = -1/4
y = mx+b
-1 = (-1/4)(-3) + b
b = -1 - (3/4)
b = -7/4
Equation: y = (-1/4)x -(7/4)
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Find coordinates of E, which is the intersection of AE and CD.
Equation of CD:
slope = 4 ; D(0,-6)
y = 4x-6
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Solve: for the intersection:
4x-6 = (-1/4)x -(7/4)
(17/4)x = 17/4
x = 1
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Solve for "y":
y = 4x-6
y = 4-6 = -2
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E(1,-2)
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cheers,
Stan H.
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