Question

HURRY PLZ

What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. 7.81 8.17 8.58 10.4

What is the exact distance from (−5, 1) to (3, 0)?

square root of 63. units square root of 65. units
square root of 67. units
square root of 69. units

Answer 1

Answer:

distance between (-4,0) to (2,5) is 7.81

and

the exact distance from (−5, 1) to (3, 0) is square root of 65. units

Answer 2

1. The distance from (-4,0) to (2,5) is 7.81 units.

2. The exact distance from (-5,1) to (3,0) is square root of 65 units.

Step-by-step explanation:

1.  Given : Two points (-4,0) and (2,5)

   To find : The distance from the point (-4,0) to (2,5)

   Let P (-4,0) and Q (2,5) be the two points then the distance from P to Q is given by, $PQ = \sqrt{(x_{2} - x_{1}  )^{2} + (y_{2} - y_{1}  )^{2}  }$

Here $x_{1} = -4  , x_{2} = 0 , y_{1} = 2 ,  y_{2} = 5$

∴ $PQ = \sqrt{(2-(-4))^{2} + (5-0)^{2}  } \\PQ = \sqrt{(2+4)^{2} + (5)^{2}  } \\PQ = \sqrt{(6)^{2} + (5)^{2} } \\PQ = \sqrt{36+25}\\PQ = \sqrt{61} \\PQ = 7.81$ units.

Hence the distance from (-4,0) to (2,5) is 7.81 units.

2.Given : Two points (-5,1) and (3,0)

   To find : The distance from the point (-5,1) to (3,0)

   Let A (-5,1) and B (3,0) be the two points then the distance from A to B is given by $PQ = \sqrt{(x_{2} - x_{1}  )^{2} + (y_{2} - y_{1}  )^{2}  }$

Here $x_{1} = -5,  x_{2} = 1,  y_{1} = 3,  y_{2} = 0$

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

$AB = \sqrt{(3-(-5))^{2} + (0-1)^{2}  }$

$AB = \sqrt{(3+5)^{2} + (-1)^{2}  }$

$AB = \sqrt{(8)^{2} + (-1)^{2}  }$

$AB = \sqrt{64 + 1}\\AB = \sqrt{65}$ units

Hence the exact distance from (-5,1) to (3,0) is square root of 65 units.