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# the type of quadrilateral

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I am being asked to determine the type of quadrilateral defined by the point of intersection (using geometry & algebra) of the lines:

x - 4y + 3 = 0
5x - y - 8 = 0
x - 4y -16 = 0
6x - 5y - 1 = 0

© BrainMass Inc. brainmass.com October 4, 2022, 1:09 pm ad1c9bdddf

## SOLUTION This solution is FREE courtesy of BrainMass!

x - 4y + 3 = 0 --equation 1
5x - y - 8 = 0 --equation 2
x - 4y -16 = 0 --equation 3
6x - 5y - 1 = 0 --equation 4
Express all equation in terms of y. That would mean only y is found in the left side of the equation.

---------------------equation 1
x - 4y + 3 = 0
- 4y = -x -3
y = (x+3)/4

Assign values for x then solve for y as shown in the table
x -3 1 5
y 0 1 2
Graph these points and connect with a straight line.

---------------------equation 2
5x - y - 8 = 0
- y = -5x + 8
y = 5x - 8
Assign values for x then solve for y as shown in the table
x 0 1 2 3
y -8 -3 2 7
Graph these points and connect with a straight line.

---------------------equation 3
x - 4y -16 = 0
-4y = -x +16
y = (x - 16)/4
Assign values for x then solve for y as shown in the table
x -4 0 4
y -5 4 3
Graph these points and connect with a straight line.

---------------------equation 4
6x - 5y - 1 = 0
- 5y = -6x + 1
y = (6x-1)/5
Assign values for x then solve for y as shown in the table
x -4 -2 1 3
y -5 -2.6 1 3.4
Graph these points and connect with a straight line.

The graph of the four lines is shown below. The bounded area formed by the intersection of the lines is a TRAPEZOID !
Take note that the two sides are parallel.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 4, 2022, 1:09 pm ad1c9bdddf>