Verify whether P(-2,2) , Q(2,2) and R(2,7) are the vertices of a
right angled triangle or not by completing the following acitvity.
` PQ= sqrt([2-(-2)]^(2) + (2-2)^(2)) = square ` …(1)
`QR = sqrt((2-2)^(2) + 97-2)^(2)) = 5` …(2)
` PR = sqrt([2-(-2)]^(2) + (7-2)^(2))= square ` ...(3)
from (1),(2),(3)
` PR^(2) = square , QP^(2) + QR^(2) = square `
` therefore PR^(2) square PQ^(2) + QR^(2)[ = or ne ]`
` therefore triangle "PQR" square ` a right angled triangle [is /is not]

Explanation

With verification `P(-2,2),Q(2,2)` and `R(2,7)`
By distance formula.
`PQ=sqrt([2-(-2)]^(2)+(2-2)^(2))`
`:.PQ=sqrt(4^(2)+0^(2))`
`:.PQ=sqrt(16)`
`:.PQ=4` ………….1
`QR=sqrt((2-2)^(2)+(7-2)^(2))`
`:.QR=sqrt(0^(2)+5^(2))`
`:.QR=sqrt(25)`
`:.QR=5`........2
`PR=sqrt([2-(-2)]^(2)+(7-2)^(2))`
`:.PR=sqrt(4^(2)+5^(2))`
`:.PR=sqrt(16+25)`
`:.PR=sqrt(41)`
`PQ^(2)+QR^(2)=4^(2)+5^(2)=16+25=41`
.......[From 1 and 2 ] ..........3
`PR^(2)=(sqrt(41))^(2)=41`...............4
`:.PQ^(2)+QR^(2)=PR^(2)` ......[From 3 and 4 ]
`:.` by converse of Pythagoras theorem,
`DeltaPQR` is a right angled triangle.
i.e. `P(-2,2),Q(2,2) and `R(2,7)` are the vertices of a right angled triangle.