Question 144201: 1.Prove that the points A(6,-13),B(-2,2),C(13,10), and D (21,-5) are vertices of a Square (hint: take note of the characteristics of a square). also, find the length of a diagonal.
2.One end of a line segment is the point, (6,-2)and the midpoint is (-1,5). find the coordinates of the other end of the line segment.
3.Find the solution set of the inequality and write its interval notation. show the S.S. on the real number line
[ (2t+5) / (t+1) ] _> 1
4. Show that the 2 inequalities are equivalent
[ (4x+3)-11] < 1/2 and [x-2] < 1/8
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1.Prove that the points A(6,-13),B(-2,2),C(13,10), and D (21,-5) are vertices of a Square (hint: take note of the characteristics of a square). also, find the length of a diagonal.
If it's a square, the 4 lengths will be the same. Check that first.
   
All 4 sides are the same length, 17, the square of 289.
Showing that any one of the angles is 90 degs is sufficient to prove it's a square. Do that by showing that the slope of AB is the negative inverse of BC.
Slope m of AB = (2 - (-13))/(-2 - 6) = 15/(-8) = -15/8
Slope m of BC = (10 - 2)/(13 - (-2)) = 8/15
AB is perpendicular to BC, so it has to be a square.
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2.One end of a line segment is the point, (6,-2)and the midpoint is (-1,5). find the coordinates of the other end of the line segment.
The difference in X and Y will be the same from the midpoint to the other end.
Diff X = 7, Diff y = -7.
The other end is the midpoint minus the Diff's.
(-1-7,5+7) or (-8,12)
Draw it and it'll make sense.
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