Question 1091375: Show that point (0,-1),(6,7),(-2,3),(8,3) are vertics of rectangle
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Call the quadrilateral ABCD, with A(0,-1), B(-2,3), C(6,7), and D(8,3). The quadrilateral is a rectangle if all the angles are right angles; the angles are right angles if adjacent sides are perpendicular to each other; adjacent sides are perpendicular to each other if their slopes are negative reciprocals.
So find the slope of each side of the quadrilateral. I think drawing a sketch is easier (and less prone to careless errors) than using the formula for the slope of a line segment between two points.
The slope of AB is -2; the slope of BC is 1/2. Since (-2)(1/2) = -1, AB and BC are perpendicular.
Find the slopes of CD and DA to finish showing that the figure is a rectangle.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Show that point (0,-1),(6,7),(-2,3),(8,3) are vertics of rectangle
If this is a rectangle, adjacent sides are perpendicular to each other. For adjacent sides to be perpendicular to each other, their slopes MUST be NEGATIVE reciprocals of each other.
In other words, if the rectangle is named ABCD, with A being (0,- 1), B being (8, 3), C being (6, 7), and D, (- 2, 3), AB and CD MUST be perpendicular to BC and AD.
Additionally, you'd need to find the length of the sides, and if AB = CD, and AD = BC, then this is DEFINITELY a rectangle.
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