Answer:
Area of ΔXYZ = 10 square units
Step-by-step explanation:
Area of the triangle XYZ = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
Height of the triangle = AY
Base of the triangle = XZ
To get the length of any segment we will use the formula,
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2)}[/tex]
Here [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the segment.
Length of AY = Distance between (-1, 4) and (3, 6)
= [tex]\sqrt{(6-4)^2+(3+1)^2}[/tex]
= [tex]\sqrt{20}[/tex]
Length of XZ = [tex]\sqrt{(6-2)^2+(-2-0)^2}[/tex]
= [tex]\sqrt{20}[/tex]
Area of ΔXYZ = [tex]\frac{1}{2}(\sqrt{20})(\sqrt{20})[/tex]
= 10 square units
