Name the type of triangle formed by the points A (-5,6) , B (-4,-2) and C (7,5).

Explanation

To find the type of triangle , first we determine the length of all three sides and see whatever condition of triangle is sarisfy by these sides.
Now , using distance formula between two points,
AB `=sqrt((-4+5)^(2)+(-2-6)^(2))`
`=sqrt((1)^(2)+(-8)^(2))`
`=sqrt(1+64)=sqrt(65)` " " `[:'d=sqrt((x_(2)-x_(1))+(y_(2)-y_(1))^(2))]`
BC `=sqrt((7+4)^(2)+(5+2)^(2))=sqrt((11)^(2)+(7)^(2))`
`=sqrt(121+49)=sqrt(170)`
and CA `=sqrt((-5-7)^(2)+(6-5)^(2))=sqrt((-12)^(2)+(1)^(2))`
`=sqrt(44+1)=sqrt(145)`
We see that, `ABneBCneCA`
and not hold the condition of Pythagoras in a `triangleABC`.
i.e., `("Hypotenuse")^(2)=("Base")^(2)+("Perpendicular")^(2)`
Hence , the required triangle is scalene because all of its sides are not equal i.e., different to each other.