Prove that the quadrilateral with given vertices is a rectangle.
Given:
Vertices are
Formula Used:
Slope of a line is given by
Slopes of parallel lines are equal.
Slopes of perpendicular lines are negative reciprocal of each other.
The opposite sides of a rectangle are parallel and each interior angle is 90 degrees.
Calculation:
The given vertices of the
The slope of the line joining the points
Now, the slope of the line with points
Since, these two slopes are negative reciprocal to each other. Hence, the line joining these points are perpendicular to each other.
Now, the slope of the line with points
Now, the slope of the line with points
Slopes
Hence, the lines joining these points are parallel to each other.
Therefore, we can see that these points satisfying the properties of a rectangle.
Hence, we can conclude that these vertices are of a rectangle.
Chapter 2 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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