Question

show that P(-3/2,3) Q(6,-2) R(-3,4) are collinear

Answer 1

these r not collinear statement error

Answer 2

The points P(-3/2,3)  Q(6,-2) and R(-3,4)  are collinear  

Given:

P(-3/2,3)  Q(6,-2) and R(-3,4)  

To find:

Show that  P(-3/2,3)  Q(6,-2) and R(-3,4)  are collinear  

Solution:

Note:

Collinear points are those which are lies on same line  

Therefore, if  the given points are collinear then they will form the lines

PQ, QR and RP and the slopes of lines will be equal

⇒ Slope of PQ =  Slope of QR

Slope of PQ = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$  = $\frac{-2 - 3}{6 + 3/2 }$  = $\frac{-5}{15/2 }$ = $\frac{-10}{15 }$ = $- (\frac{2}{3 })$  

Slope of QR = $\frac{4 +2 }{-3 - 6} }$ = $\frac{6 }{-9} }$ = $-(\frac{2 }{3} })$  

here slope of PQ = slope of QR

⇒ Therefore, the given points P, Q and R will lie on same line

⇒  The points P(-3/2,3)  Q(6,-2) and R(-3,4)  are collinear  

Hence it is proven that P(-3/2,3) Q(6,-2) and R(-3,4) are collinear  

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