Question 148059: 1) The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral. Prove that the quadrilateral is a parallelogram. (Show that line AB ll line DC and line AD ll BC)
2) The points T(-1,4), E(2,4), and D(2,-1) are vertices of a triangle. Prove that the triangle is a right triangle. (Find the slopes of line TE, line ED and line TD.)
3) The points L(3,1), O(2,-3), V(-2,-2) and E(-1,2) are vertices of a rhombus. Show that the diagonal are perpendicular.
4) Solve y = mx + b for x. Use the result to find x in y = 4x – 5 when y = 3.
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! I'll show you how to do question 1. Questions 2 and 3 are use the same technique - so you can solve them.
1) (The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral. Prove that the quadrilateral is a parallelogram.
You need to remember that parallel lines have the same slope and perpendicular lines have slopes that are negative reciprocal (the product of the slopes of two perpendicular lines equals -1.
So find the slopes is the segments AB and CD. Then find the slopes of segments BC and DA.
slope when given two points. 
Slope of AB is given by  = 
Slope of CD is given by  =
Both are 0, so they are parallel
Slope of BC is given by  = 
Slope of DA is given by  =
Both are -2/3, so they are parallel too.
A figure with two sets of parallel lines is a a prallelogram
2) For problem two, find the slopes of the three segments. Then verify that two of those slopes have a product of -1.
3)For problem three, find the slopes of the segments LV and OE. The show they have a product of -1
4)  Solve for x
Solve when y = 3, m=4 and b = -5
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