d = √(x₂ - x₁)² + (y₂ - y₁)² Distance Formula
d AD = √(2+2)² + (1-1)²
d AD = √4² + 0²
d AD = √16 + 0
d AD = √16
d AD = 4
Distance of segment AD: 4
d DC = √(4-2)² + (1-1)²
d DC = √(2)² + (0)²
d DC = √4 + 0
d DC = 2
Distance of segment DC: 2
From this information, we can draw the conclusion that segment AC must equal 6 units using the segment addition postulate.
Now, we need to find the height of the altitude. We don't even need to use the distance formula to figure out that the height is 3 units. I just wanted to incorporate algebra into my answer for fun! I love algebra.
From here, use the formula for the area of a triangle.
A = 1/2(b)(h)
A = 1/2(6)(3)
A = 9 units
The area of this triangle is 9 units. Hope this helps! :D
