The question in the image asks to plot and connect the points $A(-6, 6)$, $B(4, 6)$, $C(4, -4)$, and $D(-6, -4)$, then find the perimeter of the resulting figure.

Let's break down the solution:

Step 1: Analyze the Points

• $A(-6, 6)$
• $B(4, 6)$
• $C(4, -4)$
• $D(-6, -4)$

These points describe a rectangle, as the opposite sides are parallel to the coordinate axes.

Step 2: Distance Between Points

We can find the distance between consecutive points using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• Distance $AB$: $d = \sqrt{(4 - (-6))^2 + (6 - 6)^2} = \sqrt{(4 + 6)^2} = \sqrt{10^2} = 10$

• Distance $BC$: $d = \sqrt{(4 - 4)^2 + (-4 - 6)^2} = \sqrt{(-4 - 6)^2} = \sqrt{(-10)^2} = 10$

• Distance $CD$: $d = \sqrt{(-6 - 4)^2 + (-4 - (-4))^2} = \sqrt{(-6 - 4)^2} = \sqrt{(-10)^2} = 10$

• Distance $DA$: $d = \sqrt{(-6 - (-6))^2 + (6 - (-4))^2} = \sqrt{(6 + 4)^2} = \sqrt{10^2} = 10$

Step 3: Perimeter of the Rectangle

The perimeter $P$ of a rectangle is the sum of the distances around it: $P = AB + BC + CD + DA = 10 + 10 + 10 + 10 = 40$

Conclusion:

The perimeter of the resulting rectangle is 40 units.

Would you like more details on any part of this solution?

Here are five related questions to expand on the topic:

1. What is the area of the rectangle formed by the given points?
2. How do you find the distance between two points in a 3D coordinate system?
3. How would the solution change if one of the points were moved to another location?
4. How can you find the diagonal length of the rectangle using the Pythagorean theorem?
5. How do you identify whether four points form a parallelogram, trapezoid, or another shape?

Tip: When dealing with problems involving distance between points, always use the distance formula and double-check your coordinates.