Answer:
Area of ΔABC = 10 square units
Step-by-step explanation:
Distance between the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is represented by,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of AB = [tex]\sqrt{(-4-2)^2+(-6+8)^2}[/tex]
= [tex]\sqrt{36+4}[/tex]
= [tex]2\sqrt{10}[/tex]
Length of CD = [tex]\sqrt{(-6+7)^2+(-2+5)^2}[/tex]
= [tex]\sqrt{1+9}[/tex]
= [tex]\sqrt{10}[/tex]
Area of a triangle ABC will be represented by the formula,
Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(AB)(CD)[/tex]
= [tex]\frac{1}{2}(2\sqrt{10})(\sqrt{10})[/tex]
= 10 square units
