Respuesta :

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

Answer:

10 square units

Step-by-step explanation:

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