To analyze the figure represented by the points A(-5, 8), B(1, 5), and C(-5, 0), we can follow these steps:
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Identify the Vertices: The points represent vertices of a geometric figure. In this case, since points A and C share the same x-coordinate (-5), we can infer that the figure might be a triangle or a vertical line segment.
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Plot the Points: Plotting the points on a Cartesian coordinate system:
- Point A is located at (-5, 8)
- Point B is at (1, 5)
- Point C is at (-5, 0)
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Examine the Triangle: The points do not form a straight line; hence they do indeed form a triangle. Points A and C form a vertical side of the triangle while point B extends to the right.
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Calculate the Area: To find the area of the triangle formed by these points, we can use the formula for the area of a triangle given by vertices \((x_1, y_1)\), \((x_2, y_2)\), \((x_3, y_3)\):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Using:
- A(-5, 8)
- B(1, 5)
- C(-5, 0)
Substituting the coordinates into the formula:
\[ \text{Area} = \frac{1}{2} \left| -5(5 - 0) + 1(0 - 8) + -5(8 - 5) \right| \]
Calculating each term:
- \(-5(5 - 0) = -25\)
- \(1(0 - 8) = -8\)
- \(-5(8 - 5) = -15\)
So, adding these values gives:
\[ \text{Total} = -25 - 8 - 15 = -48 \]
Taking the absolute value, we have:
\[ \text{Area} = \frac{1}{2} \left| -48 \right| = \frac{48}{2} = 24 \]
Thus, the area of the triangle formed by the points A, B, and C is 24 square units.