To determine the area of the shape ABLU, we need to know what type of shape it is. Since only three coordinates are given (B, L, and U), I will assume the shape formed by those three points is a triangle. If the shape ABLU is not a triangle, or if it has a fourth vertex 'A' that is not provided, we cannot accurately calculate the area without additional information.
If ABLU is indeed a triangle, we can use the coordinates of points B, L, and U to calculate the area. Let's call the triangle BLU.
Here are the coordinates for the vertices of triangle BLU:
B(-3, -2)
L(-2, 5)
U(1, 1)
We can use the determinant (also known as the shoelace formula) to calculate the area of triangle BLU. The formula to find the area of a triangle given the coordinates of its vertices [tex]\((x_1, y_1)\)[/tex], [tex]\((x_2, y_2)\)[/tex], and [tex]\((x_3, y_3)\)[/tex] is as follows:
[tex]\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\][/tex]
Plugging in our coordinates:
[tex]\[
\text{Area} = \frac{1}{2} \left| (-3)(5 - 1) + (-2)(1 + 2) + (1)(-2 - 5) \right|
\][/tex]
[tex]\[
\text{Area} = \frac{1}{2} \left| (-3)(4) + (-2)(3) + (1)(-7) \right|
\][/tex]
[tex]\[
\text{Area} = \frac{1}{2} \left| -12 - 6 - 7 \right|
\][/tex]
[tex]\[
\text{Area} = \frac{1}{2} \left| -25 \right|
\][/tex]
Thus, the area of triangle BLU is:
[tex]\[
\text{Area} = \frac{1}{2} (25)
\][/tex]
[tex]\[
\text{Area} = 12.5
\][/tex]
Therefore, if ABLU is a triangle with vertices B, L, and U, its area is 12.5 square units. If the shape requires rounding to the nearest tenth, the area remains 12.5 as there are no extra decimal places to consider.
