Question

perimeter of por with vertices p(-2,9) o(7,-3) and r(-2,-3) in the coordinate plane

Answer 1

Use the distance formula to find the length of the sides and sum them up
$|PO|= \sqrt{(7 - - 2) {}^{2} + ( - 3 - 9) {}^{2} }$
$|PO|= \sqrt{(7 + 2) {}^{2} + ( -3 - 9) {}^{2} }$
$|PO|= \sqrt{(9) {}^{2} + ( - 12) {}^{2} }$
$|PO|= \sqrt{81+ 144 }$
$|PO| = \sqrt{225}$
$|PO| = 15 \: units$
Also,

$|PR|=\sqrt{( - 2 + 2) {}^{2} + ( - 3 - 9) {}^{2} }$
$|PR|=\sqrt{( 0) {}^{2} + ( - 12) {}^{2} }$
$|PR|=\sqrt{0+ 144 }$
$|PR| = \sqrt{144}$
$|PR|=12 \: units$

And

$|OR|=\sqrt{( - 2 - 7) {}^{2} + ( - 3 + 3) {}^{2} }$
$|OR|=\sqrt{( - 9) {}^{2} + ( 0) {}^{2} }$
$|OR|=\sqrt{0+ 81 }$
$|OR|=\sqrt{81}$
$|OR|=9 \: units$

Hence perimeter triangle POR
$= 15 + 12 + 9$
$= 36 \: units$