Question

triangle jkl has purchases at the following coordinates J (2, 2) K( -1, 3) and L (-2,-1) determine whether or not triangle jkl is a right triangle show all calculations for full credit

Answer 1

It seems the triangle is rectangle, we will see if its true verifying via the pythagoras theorem

`\begin{gathered} \text{The pytagoras theorem states that} \\ a^2+b^2=c^2 \\ \end{gathered}`

`\begin{gathered} \text{ So we must calculate a, b, and c. } \\ a=d(K,L)=\sqrt[]{(-1-(-2))^2+(3-(-1))^2}^{} \\ a=\sqrt[]{1+16}=\sqrt[]{17} \\ \\ b=d(K,J)=\sqrt[]{(-1-(2))^2+(3-(2))^2} \\ b=\sqrt[]{9+1}=\sqrt[]{10} \\ \\ c=d(J,L)=\sqrt[]{(2-(-2))^2+(2-(-1))^2} \\ c=\sqrt[]{16+9}=\sqrt[]{25}=5 \end{gathered}`

And now we see a^2 +b^2 = c^2

`\begin{gathered} a^2+b^2=17+10=27 \\ c^2=25, \\ \text{ Since 27}\\e25, \\ a^2+b^2\\e c^2 \end{gathered}`

And the triangle is not right triangle