Find the area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4).

Solution:

The given coordinates are (-3, -4), (-7, 0), and (-3, 4)

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

Substituting the values in the formula

= 1/2 |-3 (0 - 4) - 7 (4 + 4) - 3 (-4 - 0)|

By further calculation

= 1/2 |-3 (-4) - 7 (8) - 3 (-4)|

= 1/2 |12 - 56 + 12|

So we get

= 1/2 |24 - 56|

= 1/2 (32)

= 16

Therefore, the area of the triangle is 16 square units.

Find the area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4).

Summary:

The area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4) is 16 square units.