Answer:
[tex]\frac{13}{2}[/tex] square units
Step-by-step explanation:
We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).
We have to find the area of triangle.
We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]
[tex]x_1=3,x_2=5,x_3=6[/tex]
[tex]y_1=1,y_2=4,y_3=-1[/tex]
Substitute the values in the formula then we get
Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units
