Match each pair of points with the approximate distance between them. Round your answers to the nearest tenth. 7.07 units 5.1 units 2 units 2.83 units 5.39 units 13.15 units 12.5 units (3, -1) and (5, 4) (2, 3) and (4, 5) (-5, 7) and (8, 5) (-2, 4) and (3, -1)

(3, -1) -> (5, 4) = √29 or 5.38516

(2, 3) -> (4, 5) = 2√2 or 2.82843

(-5, 7) -> (8, 5) = √173 or 13.1529

(-2, 4) -> (3, -1) = 5√2 or 7.07107

Step-by-step explanation:

Distance Formula:

Simply plug the coordinates into the distance formula:

To get the decimals, we evaluate the square roots:

√29 = 5.38516

2√2 = 2.82843

√173 = 13.1529

5√2 = 7.07107

d = √[(x₂ - x₁)² + (y₂-y₁)²]

(3, -1) and (5, 4)

√(5−3)²+(4-(-1)²

√(2)²+(5)²

√4+25

√29 = 5.385164807134504 = 5.39

(2,3) and (4,5)

√(4-2)v+(5−3)²

√(2)²+(2)²

√4+4

√8 ≈2.8284271247461903 = 2.83

(-5, 7) and (8,5)

√(8−−5)²+(5−7)²

√(8++0)2+(5−7)²

√(13)²+(−2)²

√169+4

√173 ≈ 13.152946437965905 = 13.15

(-2, 4) and (3, -1)

(3− −2)²+(−1−4)²

√(3++0)²+(−1−4)²

√(5)² + (−5)²

√25+25

√50 ≈ 7.0710678118654755 = 7.07

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation:

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