Answer:
The approximate area, of the baseball diamond is 8192 ft²
Step-by-step explanation:
The given coordinates of the baseball diamond are;
(0, 64), (64, 0), (0, -64), and (-64, 0)
The length of one unit of the coordinate plane = 1 foot
Therefore, we note that, there are two points with x-coordinate = 0 at which the y-coordinates = 64 and -64
Similarly here are two points with y-coordinate = 0 at which the x-coordinates = 64 and -64
The length of the segment are therefore the vertices of a square as we have;
A(0, 64), B(64, 0), C(0, -64), and D(-64, 0)
∠DBA = ∠DCA = tan⁻¹(64/64) = tan⁻¹(1) = 45°
∠DBA + ∠DCA = ∠ABC = 90°
The shape of the diamond is a square
The length, l of the side of the square is given by the relation;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
When, (x₁, y₁) = (0, 64), (x₂, y₂) = (64, 0)
We have;
[tex]l = \sqrt{\left (0 -64 \right )^{2}+\left (64-0 \right )^{2}} = 64\cdot \sqrt{2}[/tex]
The
The area, A, of the baseball diamond is therefore;
A = Area of a square = (Length of the side of a square)² = (64·√2)² = 8192 ft²
The area, of the baseball diamond = 8192 ft².
