Question

this figure represents what? and the area.
A (-5,8)
B(1,5)
C(-5,0)

Answer 1

To analyze the figure represented by the points A(-5, 8), B(1, 5), and C(-5, 0), we can follow these steps:

1. **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.

2. **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)

3. **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.

4. **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:

1. \(-5(5 - 0) = -25\)
2. \(1(0 - 8) = -8\)
3. \(-5(8 - 5) = -15\)

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**.