Given the points A (1,8), (4,7) and (0,0), find the area of triangle ABC. Plot the points A,B,C and O on the Cartesian plane and draw triangle ABC?

To find the area of triangle ABC, we can use the formula for the area of a triangle given its vertices:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Given the points A (1,8), B (4,7), and C (0,0), we can plug in the coordinates into the formula:

Area = 1/2 * |1(7 - 0) + 4(0 - 8) + 0(8 - 7)|
Area = 1/2 * |7 - 32 + 0|
Area = 1/2 * |-25|
Area = 12.5

Therefore, the area of triangle ABC is 12.5 square units.

To plot the points A (1,8), B (4,7), and C (0,0) on the Cartesian plane and draw triangle ABC, follow these steps:

1. Plot point A at (1,8)
2. Plot point B at (4,7)
3. Plot point C at (0,0)
4. Connect the points A, B, and C with lines to form triangle ABC

The triangle ABC should look like this on the Cartesian plane:

A (1,8)
B (4,7)
C (0,0)

Now, you can draw the triangle by connecting the points A, B, and C with lines.

Calculating the Area of Triangle ABC

Using the shoelace formula:

```
Area = (1/2) | (x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3) |
```

where (x1, y1) = (1, 8), (x2, y2) = (4, 7), (x3, y3) = (0, 0)

```
Area = (1/2) | (1-7 + 4-0 + 0-8 - 4-8 - 0-1 - 1-0) |
Area = (1/2) | -28 |
Area = 14 square units
```

Plotting the Points and Drawing Triangle ABC

[Image of Cartesian plane with points A, B, C, and O labeled]

- Plot point A at (1, 8)
- Plot point B at (4, 7)
- Plot point C at (0, 0)
- Plot point O at (0, 0)

Connect points A, B, and C to form triangle ABC.