Answer:
37.5 square units
Step-by-step explanation:
Given:
A(-6,-4), B(6,5), C(-1,6), and D(2, 2), where CD is the altitude if ∆ABC
Required:
Area of ∆ABC
SOLUTION:
Area of a ∆ABC =½*AB*CD
✍️[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{6 -(-6))^2 + (5 -(-4))^2 [/tex]
[tex] AB = \sqrt{12^2 + 9^2} [/tex]
[tex] AB = \sqrt{144 + 81} [/tex]
[tex] AB = \sqrt{225} = 15 [/tex]
✍️[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{2 -(-1))^2 + (2 - 6)^2 [/tex]
[tex] CD = \sqrt{(3)^2 + (-4)^2} [/tex]
[tex] CD = \sqrt{9 + 16} [/tex]
[tex] CD = \sqrt{25} = 5 [/tex]
✍️Area of a ∆ABC =½*AB*CD
= ½*15*5
✅ Area = 37.5 square units
