Points: (5,2), (- 1,0 ), or (3,- 4) Explanation: See solution.
Practice makes perfect
We are given the coordinates of three vertices of a parallelogram.
A(2,1), B(1, - 2), and C(4,- 1)
Let's plot these points on a coordinate plane.
Depending on how we connect the three vertices, there are three possible locations for the point D. Let's take a look at each case separately.
Case I
Let's assume that AB and BC are two sides of the parallelogram. To find the coordinates of point D, we will use the slope of one of the sides, as, by definition, the opposite sides of a parallelogram are parallel and are of equal length.
We see that the slope of BC is 13.
Slope=Rise/Run ⇔ Slope= 1/3
Now, starting at A and using the rise and run, we can find the coordinates of D.
The fourth vertex D occurs at the point (5,2) if AB and BC are two sides of the parallelogram. Let's draw the parallelogram.
Case II
This time, we will assume that AC and CB are two sides of the parallelogram. We will find the coordinates of point D similarly. Let's use the slope of CB.
We see that point D is located at (- 1,0).
Case III
Finally, we will assume that AB and AC are two sides of the parallelogram. To find the coordinates of the point D, we will use the slope of AC.
We see that point D is located at (3,- 4). As a result, we have found three different points that can form a parallelogram with the points A, B, and C.
D(5,2), D(- 1,0 ), or D(3, - 4)
