Which of the following points are more than 5 units from the point P(−2, −2)? Select all that apply. A A (2, 1) B B (4, −1) C C (2, −3) D D (−6, −6) E E (−5, 1)

Question

asked Jul 13, 2018 35.2k views

1 Answer

Manas Pratim Chamuah · Answer 1 · 2018-07-16T12:29:23+0000

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

$|PQ|= \sqrt{ (a-c)^(2) + (b-d)^(2)}$

Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.

$|PA|= \sqrt{ (-2-2)^(2) + (-2-1)^(2)}= √(16+9)= √(25)=5$

$|PB|= \sqrt{ (-2-4)^(2) + (-2+1)^(2)}= √(36+1)= √(37) \approx 6$

$|PC|= \sqrt{ (-2-2)^(2) + (-2+3)^(2)}= √(16+1)= √(17)\approx4$

$|PD|= \sqrt{ (-2+6)^(2) + (-2+6)^(2)}= √(16+16)= √(32)\ \textgreater \ √(25)=5$

$|PE|= \sqrt{ (-2+5)^(2) + (-2-1)^(2)}= √(9+9)= √(16)=4$

Answer: B and D