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Solved on Nov 06, 2023

Find the distance between the given points using the distance formula. Round to the nearest hundredth. 9) (0,3)(0,3) and (4,−9)(4,-9): (4−0)2+(−9−3)2≈12.04\sqrt{(4-0)^2 + (-9-3)^2} \approx 12.04 12) (−1,5)(-1,5) and (4,5)(4,5): (4−(−1))2+(5−5)2=5\sqrt{(4-(-1))^2 + (5-5)^2} = 5 10) (−6,16)(-6,16) and (11,−2)(11,-2): (11−(−6))2+(−2−16)2≈19.08\sqrt{(11-(-6))^2 + (-2-16)^2} \approx 19.08 13) (14,2)(14,2) and (−2,−2)(-2,-2): (14−(−2))2+(2−(−2))2≈16.12\sqrt{(14-(-2))^2 + (2-(-2))^2} \approx 16.12 11) (−8,7)(-8,7) and (10,4)(10,4): (10−(−8))2+(4−7)2≈18.03\sqrt{(10-(-8))^2 + (4-7)^2} \approx 18.03 14) (−5,6)(-5,6) and (−5,7)(-5,7): (−5−(−5))2+(7−6)2=1\sqrt{(-5-(-5))^2 + (7-6)^2} = 1

STEP 1

Assumptions1. The points given are in the form (x, y) . The distance formula is derived from the Pythagorean theorem and is given byd = \sqrt{(x - x1)^ + (y - y1)^}3. The distances are to be rounded to the nearest hundredth

STEP 2

Let's start with the first pair of points (0,)(0,) and (4,−9)(4,-9). We can plug these values into the distance formula.
d=(4−0)2+(−9−)2d = \sqrt{(4 -0)^2 + (-9 -)^2}

STEP 3

implify the equation.
d=()2+(−12)2d = \sqrt{()^2 + (-12)^2}

STEP 4

Calculate the squares.
d=16+144d = \sqrt{16 +144}

STEP 5

Add the numbers under the square root.
d=160d = \sqrt{160}

STEP 6

Calculate the square root and round to the nearest hundredth.
d≈12.65d \approx12.65

STEP 7

Repeat the process for the next pair of points (−1,5)(-1,5) and (4,5)(4,5).
d=(4−−1)2+(5−5)2d = \sqrt{(4 - -1)^2 + (5 -5)^2}

STEP 8

implify the equation.
d=(5)2+(0)2d = \sqrt{(5)^2 + (0)^2}

STEP 9

Calculate the squares.
d=25+d = \sqrt{25 +}

STEP 10

Calculate the square root.
d=5d =5

STEP 11

Continue this process for all remaining pairs of points. For example, for the pair (−6,16)(-6,16) and (11,−)(11,-)d = \sqrt{(11 - -6)^ + (- -16)^}

STEP 12

implify the equation.
d=(17)2+(−18)2d = \sqrt{(17)^2 + (-18)^2}

STEP 13

Calculate the squares.
d=289+324d = \sqrt{289 +324}

STEP 14

Add the numbers under the square root.
d=613d = \sqrt{613}

STEP 15

Calculate the square root and round to the nearest hundredth.
d≈24.76d \approx24.76The distances between the points are approximately12.65,5, and24.76 respectively.

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