# Desmos showing algebraically that rectangle has perpendicular sides

#### sirnam505

##### New member

These are linear inequalities that only leave interior of rectangle as white space. They are:

. . . . .$$\displaystyle y\, <\, 5x$$

. . . . .$$\displaystyle y\, >\, 5x\, +\, 2$$

. . . . .$$\displaystyle x\, >\, -5y$$

. . . . .$$\displaystyle x\, <\, -5y\, -\, 2$$

No vertical or horizontal lines were allowed to make this.
I need to be able to show algebraically or numerically that the rectangle has perpendicular sides. Essentially proving that the sides are perpendicular. How would I go about doing this?

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#### Otis

##### Senior Member
Show that the slopes (in any pair of perpendicular lines) are negative reciprocals of each other.

EG:

y = 4x + 3
y = (-1/4)x - 7

The slopes are negative reciprocals, so those lines are perpendicular.

#### HallsofIvy

##### Elite Member

These are linear inequalities that only leave interior of rectangle as white space. They are:

. . . . .$$\displaystyle y\, <\, 5x$$

. . . . .$$\displaystyle y\, >\, 5x\, +\, 2$$

. . . . .$$\displaystyle x\, >\, -5y$$

. . . . .$$\displaystyle x\, <\, -5y\, -\, 2$$

No vertical or horizontal lines were allowed to make this.
I need to be able to show algebraically or numerically that the rectangle has perpendicular sides. Essentially proving that the sides are perpendicular. How would I go about doing this?
By the way- you titled this "Showing that rectangle has perpendicular sides". A rectangle by DEFINITION has perpendicular sides. What you meant was "Showing that this geometric object IS a rectangle".

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