Question 143266: we just started coordinate geometry proofs with slope, midpoint, and distance. i have the formulas for all three but i don't understand how to apply the formula to a problem.
ex) Given Points: A(2,-7) B(-3,-5) C(1,-7) D(6,-9).
1. Are lines AB and CD parallel? Are they perpendicular?
2. What is the midpoint of lines AB and CD? Do they bisect eachother? Why or why not?
3. What is the length of line AB and CD? Are they congruent?
I know this is a long problem but i don't just want the answer, i really need help understanding it all so if someone could explain it i'd appreciate that. thank youu
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! 1. Use the two-point form of the equation of a straight line to write the equations for the lines containing segments AB and CD. Then solve each of the equations for y (that is, put them in  form) If the slopes are equal, then the lines are parallel. If the slopes are negative reciprocals, i.e.  , then they are perpendicular. Otherwise neither.
2. Apply the midpoint formulas to the coordinates for A and B. Repeat for the coordinates for C and D. If you get the same set of coordinates, meaning the midpoint of AB is the same point as the midpoint of CD, then the two segments bisect each other, otherwise not.
3. Apply the distance formula to the coordinates for A and B. Do it again for the coordinates for C and D. If you get the same answer both times, the segments are congruent. Otherwise not.
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