Question

What is the area of the triangle with vertices (-4,1), (-6,-3), (5,-3)?

Answer 1

Using the Shoelace formula, the area of the triangle with vertices (-4,1), (-6,-3), and (5,-3) is 2 square units.

Step-by-step explanation:

To find the area of a triangle with given vertices, we can use the Shoelace formula or the determinant method. The vertices of the triangle given are (-4,1), (-6,-3), and (5,-3). We'll apply the formula:

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

Substituting the coordinates into the formula, we have:

1. Area = 1/2 |(-4(-3 - (-3)) + (-6)(-3 - 1) + (5)(1 - (-3)))|
2. Area = 1/2 |(0 - (-6)(-4) + (5)(4))|
3. Area = 1/2 |(0 - 24 + 20)|
4. Area = 1/2 |-4|
5. Area = 1/2 * 4
6. Area = 2 square units

The area of the triangle is 2 square units.