Question

Draw the segment PQ with endpoints P(-2, -1) and Q(2,4) on the coordinate plane. Then find the length and midpoint of PQ.

Answer 1

The graph of the line segment PQ is attached. To find the length, we have to use distance formula which is

$d = \sqrt{ (x_{2} -x_{1} )^2 + (y_{2} - y_{1} )^2 }$

$PQ = \sqrt{ (2-(-2))^2 + (4- (-1))^2 } = \sqrt{ (2+2)^2 + (4+1)^2 }$

$PQ = \sqrt{16+25} = \sqrt{41}$

To find the midpoint,we have to use the formula

$( \frac{x_{1}+ x_{2} }{2} ,\frac{y_{1}+ y_{2} }{2} ) = (\frac{-2+2}{2} , \frac{-1+4}{2} )$

$= ( \frac{0}{2} , \frac{3}{2} ) = (0 , \frac{3}{2} )$