A parallelogram is made with the lines x - y = 5, x - y = 8, x + y = 2 and x + y = 10. What is the area of the parallelogram

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The 4 sides of the parallelogram are the lines x - y = 5, x - y = 8, x + y = 2 and x + y = 10. The plot of the lines gives the parallelogram that is created.

The parallelogram created by the intersection of the given lines is a rectangle as two of them are perpendicular to the others.

To determine the area we need the length of the sides of the rectangle.

From the figure the end-points of one of the sides are (5, -3) and (9, 1). The length of this side is `<span style="font-family: Serif;" data-mce-style="font-family: Serif;">(9-5)2+(1+3)2</span>` = `<span style="font-family: Serif;" data-mce-style="font-family: Serif;">42+42</span>` = `<span style="font-family: Serif;" data-mce-style="font-family: Serif;">4⋅2</span>`

The end-points of the adjacent side are (3.5, -1.5) and (5, -3). The length of this side is`<span style="font-family: Serif;" data-mce-style="font-family: Serif;">(3.5-5)2+(-3+1.5)2=32</span>`

The area of the rectangle is A = `<span style="font-family: Serif;" data-mce-style="font-family: Serif;">4⋅2⋅32</span>` = 4*3 = 12

The area of the parallelogram formed by the given lines is 12 square units.

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