SOLUTION: The points A(0,0), B(2,4)and D(7,O) are three of the four vertices of a parallelogram. What are the coordinates of the fourth? The coordinates of three vertices of a square ar

Algebra ->  Parallelograms -> SOLUTION: The points A(0,0), B(2,4)and D(7,O) are three of the four vertices of a parallelogram. What are the coordinates of the fourth? The coordinates of three vertices of a square ar      Log On


   

Question 244194: The points A(0,0), B(2,4)and D(7,O) are three of the four vertices of a parallelogram. What are the coordinates of the fourth?

The coordinates of three vertices of a square are A(2,-3), B(-2,-1) and C(0,3). What are coordinates of the fourth vertex
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Presuming that the sides of the parallelogram are the segments AB, BC, CD, and DA, proceed thusly:

Compute the slope of the line containing the segment AB using the slope formula:



Where and are the coordinates of the endpoints of the segment.

Write an equation of the line that passes through point D with a slope equal to the slope of the line that contains the segment AB using the point-slope form of the equation of a line:



Where is the slope you just calculated and are the coordinates of D. Call this equation 1.

Repeat the above steps with respect to line segment BC and point D. Call this equation 2.

Solve the system of equations formed by equations 1 and 2. The solution set will be the desired coordinates of the fourth vertex.

Do your other problem the same way.


John