SOLUTION: Analytic Geometry 17.a) Determine the type of quadrilateral that has vertices at A(4, 6), B(-4, -2), C(2, -5), and D(11, 4). Can you please help me and thank you very much!!!#@$#

Question 200401: Analytic Geometry
17.a) Determine the type of quadrilateral that has vertices at A(4, 6), B(-4, -2), C(2, -5), and D(11, 4).
Can you please help me and thank you very much!!!#@$##
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
AB parallel to CD, slopes both equal 1,,,,,m=(y2-y1)/(x2-x1)
.
slope of BC = -1/2, slope of AB = -2/7
.
Length of AD = 7.3,,,BC=6.7,,AB = 11.3,,,CD=12,,,,,d=sqrt { (y2-y1)^2 + (x2-x1)^2 }
.
Therefore this is a trapezoid,,,,,,,,, 2 sides parallel,,,,,only
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use the formula for the slope of a line:

To calculate the slopes of the lines containing the four line segments forming the sides of your quadrilateral.

Use the distance formula to calculate the lengths of each of the four sides.

Use the fact that parallel lines have equal slopes.

If none of the slopes are equal, you have no parallel sides, so you have a general quadrilateral or a kite. If two adjacent sides have equal lengths and the other two have equal lengths, then it is a kite, otherwise it is a general quadrilateral.

If two lines have the same slope and the other two slopes are not equal, you have a trapezoid (trapezium if you are British)

If you have two pairs of equal slopes, you have a parallelogram, rhombus, rectangle, or square.

Given that, if the unequal slopes are negative reciprocals of each other, then you have a rectangle or square because the adjacent sides are perpendicular. In this case, if the lengths of two adjacent sides are equal, you have a square, otherwise it is a rectangle.

If the adjacent sides are not perpendicular, then you have a general parallelogram or a rhombus. If the lengths of two adjacent sides are equal, then you have a rhombus, otherwise it is a general parallelogram.

John

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