To graph the parallelogram with the given vertices [tex]\( (-2,9), (-7,9), (0,10), (5,10) \)[/tex], follow these steps:
1. Plot the Points: First, we need to plot the given vertices on a coordinate plane.
- Plot the point [tex]\((-2, 9)\)[/tex].
- Plot the point [tex]\((-7, 9)\)[/tex].
- Plot the point [tex]\((0, 10)\)[/tex].
- Plot the point [tex]\((5, 10)\)[/tex].
2. Connect the Vertices: After plotting the points, connect them to form the sides of the parallelogram.
- Draw a line from [tex]\((-2, 9)\)[/tex] to [tex]\((-7, 9)\)[/tex].
- Draw a line from [tex]\((-7, 9)\)[/tex] to [tex]\( (0, 10) \)[/tex].
- Draw a line from [tex]\((0, 10)\)[/tex] to [tex]\((5, 10)\)[/tex].
- Finally, draw a line from [tex]\((5, 10)\)[/tex] back to [tex]\((-2, 9)\)[/tex].
Let's go through these steps with a detailed description.
### Step 1: Plot the Points
Identify the coordinates on the coordinate plane for each vertex:
- [tex]\((-2,9)\)[/tex]: The point is at -2 units on the x-axis and 9 units on the y-axis.
- [tex]\((-7,9)\)[/tex]: The point is at -7 units on the x-axis and 9 units on the y-axis.
- [tex]\((0,10)\)[/tex]: The point is at 0 units on the x-axis and 10 units on the y-axis.
- [tex]\((5,10)\)[/tex]: The point is at 5 units on the x-axis and 10 units on the y-axis.
### Step 2: Connect the Vertices
Draw lines to form the parallelogram:
- Draw a horizontal line between [tex]\((-2, 9)\)[/tex] and [tex]\((-7, 9)\)[/tex]. Since they both share the same y-coordinate, this line is parallel to the x-axis.
- Draw an oblique line from [tex]\((-7, 9)\)[/tex] to [tex]\((0, 10)\)[/tex].
- Draw a horizontal line from [tex]\((0, 10)\)[/tex] to [tex]\((5, 10)\)[/tex]. Since they both share the same y-coordinate, this line is also parallel to the x-axis.
- Finally, draw an oblique line from [tex]\((5, 10)\)[/tex] back to [tex]\((-2, 9)\)[/tex].
By following these steps, you will have plotted and connected the points to form the parallelogram with the given vertices. Your graph should show a quadrilateral bounded by these points and their connecting lines, and you will see two parallel horizontal sides and two opposing sides connecting the vertices:
[tex]\[
\begin{align*}
A & = (-2, 9) \\
B & = (-7, 9) \\
C & = (0, 10) \\
D & = (5, 10)
\end{align*}
\][/tex]
This completes the construction and graphing of the parallelogram with the given vertices.
