Fill in the steps to find the area of the shape. Units are in yards.

Question

(0,8)

(4,2)

(-5,-4)

(-9,2)

Step 1: Find the ___
of the line that connects A to B and the line that connects ___ .

Once these are found, we will ____ these.

The final answer is ___ ___.

Answer 1

To find the area of the shape defined by the given points, let's fill in the steps.

1. Step 1: Find the lengths of the line that connects A to B (which are the points (0,8) and (4,2)) and the line that connects C to D (which are the points (-5,-4) and (-9,2)).

2. Once these are found, we will use the lengths to calculate the area of the shape formed by the points.

3. The final answer is calculated area in square yards.

To further elaborate on how to calculate the area, we would typically need to form a polygon with the points, then either use the formula (1/2) * |Σ(x_i * y_(i+1) - x_(i+1) * y_i)| or apply the Shoelace theorem to find the area based on coordinate geometry.

If you have a specific polygon or area calculation in mind based on these points, please provide the details and I can assist with that!

Answer 2

how many yards?

Answer 3

To find the area of the shape defined by the points $(0,8)$, $(4,2)$, $(-5,-4)$, and $(-9,2)$, we can apply the shoelace theorem (also known as Gauss's area formula for polygons).

Step-by-step Calculation:

1. List the coordinates in order:

   • $A(0,8)$
   • $B(4,2)$
   • $C(-9,2)$
   • $D(-5,-4)$

   We will repeat the first point at the end for the calculation:

   • $(0,8),(4,2),(-9,2),(-5,-4),(0,8)$

2. Apply the Shoelace Theorem: The formula for the area $A$ is: $$A=\frac{1}{2}|\sum _{i=1}^n(x_i{y}_{i+1}-y_i{x}_{i+1})|$$ where the last point connects back to the first.

3. Calculate the sums:

   • Sum of $x_i{y}_{i+1}$: $$(0)(2)+(4)(2)+(-9)(-4)+(-5)(8)=0+8+36-40=4$$

   • Sum of $y_i{x}_{i+1}$: $$(8)(4)+(2)(-9)+(2)(-5)+(-4)(0)=32-18-10+0=4$$

4. Combine the sums: $$A=\frac{1}{2}|4-4|=\frac{1}{2}\times 0=0$$

5. Final Result: Since the calculated area is $0$, this indicates that the points may be collinear or do not form a closed polygon with a measurable area.

Thus, the area of the shape formed by the points $(0,8)$, $(4,2)$, $(-5,-4)$, and $(-9,2)$ is 0 square yards. This means that the points do not enclose any space.