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

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=`
`√((0-(-2))^2+(-6-4)^2)=√(104)`

Distance between the points
`A` and
`T`=
`at=`
`√((-2-(3))^2+(4-5)^2)=√(26)`

Distance between the points
`T` and
`C`=
`tc=`
`√((3-0)^2+(5-(-6))^2)=√(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.