Question

Triangle CAT has vertices at C(-6,0), A(4,-2), and T(5,3). What type of triangle is CAT?

Answer 1

Right-angled triangle

Step-by-step explanation:

given point $C=(-6,0)$ ,$A=(4,-2)$ and $T=(5,3)$

Distance between any two points $p1=(x_{1},y_{1})$ and $p2=(x_{2},y_{2})$ is $\sqrt{(y_{2}-y_{1})^{2} +(x_{2}-x_{1})^{2}}$

Distance between the points $C$ and $A$=$ca=$$\sqrt{(0-(-2))^2+(-6-4)^2}=\sqrt{104}$

Distance between the points $A$ and $T$=$at=$$\sqrt{(-2-(3))^2+(4-5)^2}=\sqrt{26}$

Distance between the points $T$ and $C$=$tc=$$\sqrt{(3-0)^2+(5-(-6))^2}=\sqrt{130}$

calculate $ca^{2}+at^{2}=104+26=130$

calculate $tc^{2}$$=130$

So,$ca^{2}+at^{2}=tc^{2}$

Since,sum of squares of two sides is equal square of the third side,using pythagoras theorem

The triangle is a right angled triangle.