 |
|---|
| PAGE: 507 | SET: Exercises | PROBLEM: 36 |
The vertices of the parallelogram are 
and 
.
Need to prove that the centroid of the parallelogram is the point of intersection of the diagonals.
Draw the related parallelogram.
Find the position of the intersection of the medians.
Equation of line 
.
Point slope form of a line equation is 
.
Equation of line 
.
.
The intersection point of 
and 
.
.
Substitute 
in 
.
.
The point of intersection is 
.
Find the area of parallelogram.
The area of the parallelogram is 
.
Substitute 
and 
.
.
.
First find the curve equations:
Equation of line 
.
Point slope form of a line equation is .
.
Consider 
.
Equation of line 
:
.
Consider 
.
Find the 
-coordinate of the centroid.
.
.
.
Find the 
-coordinate of the centroid.
.
.
.
Therefore, centroid is 
.
The centroid of parallelogram is located at the point of intersection of the diagonals.
.
The centroid of any triangle is located at the point of intersection of the medians.
|
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
|
"Your site is amazing! It helped me get through Algebra." Charles |
|
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |
Simply chose a support option
  
|