To determine the shape formed by the points A(-2, 4), B(2, -4), and C(-2, -4), let's start by plotting the points:
- Point A is located at (-2, 4).
- Point B is at (2, -4).
- Point C is at (-2, -4).
Now, let's analyze the layout of these points:
-
Points A and C share the same x-coordinate (-2), which means they are vertically aligned. The distance between A and C can be computed simply by looking at the y-coordinates:
- Distance AC = |4 - (-4)| = |4 + 4| = 8.
-
Points A and B can be connected as well, and for that, we can find the distance between them using the distance formula: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ AB = \sqrt{(2 - (-2))^2 + (-4 - 4)^2} = \sqrt{(2 + 2)^2 + (-8)^2} = \sqrt{(4)^2 + (-8)^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}. \]
-
For points B and C: \[ BC = \sqrt{(2 - (-2))^2 + (-4 - (-4))^2} = \sqrt{(2 + 2)^2 + (0)^2} = \sqrt{(4)^2} = 4. \]
Now that we have found the lengths of the sides, we can summarize that:
- AC = 8 (vertical)
- AB = \( 4\sqrt{5} \) (slanted)
- BC = 4 (horizontal)
Calculating the Perimeter:
The perimeter (P) of the triangle formed by points A, B, and C is the sum of the lengths of its sides: \[ P = AB + BC + AC = 4\sqrt{5} + 4 + 8. \]
Combining these, we express the perimeter as: \[ P = 4\sqrt{5} + 12. \]
Conclusion:
The shape created by points A, B, and C is a triangle. The perimeter of this triangle is given by \( P = 4\sqrt{5} + 12 \) units.