Answered

II. Find the distance between the two given points. Write your solution on a separate paper.



__________ 1. P ( 3, 5 ) Q ( 3, - 2 )

__________ 2. A ( 0, 0 ) B ( - 4, 3 )

__________ 3. L ( - 2, 6 ) M ( - 7, 7 )

__________ 4. D ( 5, 2 ) E ( 0, - 6 )

__________ 5. R ( - 3, 1 ) S ( 3, 9 )

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✏️DISTANCES

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[tex]\underline{\mathbb{DIRECTION:}}[/tex]

- Find the distance between the two given points. Write your solution on a separate paper.

  • #1. P(3,5) and Q(3,-2)
  • #2. A(0,0) and B(-4,3)
  • #3. L(-2,6) and M(-7,7)
  • #4. D(5,2) and E(0,-6)
  • #5. R(-3,1) and S(3,9)

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[tex]\underline{\mathbb{ANSWERS:}}[/tex]

[tex]\qquad\Large\rm»\:\: 1. \: \green{PQ = 7\:units}[/tex]

[tex]\qquad\Large\rm»\:\: 2. \: \green{AB = 5\:units}[/tex]

[tex]\qquad\Large\rm»\:\: 3. \: \green{LM ≈ 5.09\:units}[/tex]

[tex]\qquad\Large\rm»\:\: 4. \: \green{DE ≈ 9.43\:units}[/tex]

[tex]\qquad\Large\rm»\:\: 5. \: \green{RS ≈ 12.04\:units}[/tex]

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[tex]\underline{\mathbb{SOLUTIONS:}}[/tex]

- Using the Distance Formula to find the distance between the given two points.

[tex]\begin{gathered} \begin{aligned} & \bold{\color{lightblue}Formula:} \\ & \boxed{ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\,}} \end{aligned} \end{gathered}[/tex]

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#1. P(3,5) and Q(3,-2)

  • [tex]PQ = \sqrt{(3 -3)^2+( \text - 2 - 5)^2}[/tex]

  • [tex]PQ = \sqrt{(0)^2+( \text -7)^2}[/tex]

  • [tex]PQ= \sqrt{0 + 49}[/tex]

  • [tex]PQ= \sqrt{49} [/tex]

  • [tex]PQ = 7[/tex]

[tex]\therefore[/tex] The distance between the point P and Q is 7 units.

[tex]\rm[/tex]

#2. A(0,0) and B(-4,3)

  • [tex]AB= \sqrt{( \text - 4 - 0)^2+(3 - 0)^2}[/tex]

  • [tex]AB= \sqrt{( \text - 4)^2+(3)^2}[/tex]

  • [tex]AB= \sqrt{16+9}[/tex]

  • [tex]AB= \sqrt{25}[/tex]

  • [tex]AB = 5[/tex]

[tex]\therefore[/tex] The distance between the point A and B is 5 units.

[tex]\rm[/tex]

#3. L(-2,6) and M(-7,7)

  • [tex]LM= \sqrt{( \text -7 - ( \text - 2))^2+(7 - 6)^2}[/tex]

  • [tex]LM= \sqrt{( \text -7 + 2)^2+(7 - 6)^2}[/tex]

  • [tex]LM= \sqrt{( \text -5)^2+(1)^2}[/tex]

  • [tex]LM= \sqrt{25+1}[/tex]

  • [tex]LM= \sqrt{26}≈5.09[/tex]

[tex]\therefore[/tex] The distance between the point L and M is √26 or approximate 5.09 units.

[tex]\rm[/tex]

#4. D(5,2) and E(0,-6)

  • [tex]DE= \sqrt{(0 - 5)^2+( \text -6 - 2 )^2}[/tex]

  • [tex]DE= \sqrt{( \text - 5)^2+( \text -8)^2}[/tex]

  • [tex]DE= \sqrt{25+64}[/tex]

  • [tex]DE= \sqrt{89}≈9.43[/tex]

[tex]\therefore[/tex] The distance between the point D and E is √89 or approximate 9.43 units.

[tex]\rm[/tex]

#5. R(-3,1) and S(3,9)

  • [tex]RS= \sqrt{(3-(\text-3))^2+(9-1)^2}[/tex]

  • [tex]RS= \sqrt{(3+3)^2+(9-1)^2}[/tex]

  • [tex]RS= \sqrt{(9)^2+(8)^2}[/tex]

  • [tex]RS= \sqrt{81+64}[/tex]

  • [tex]RS= \sqrt{145}≈12.04[/tex]

[tex]\therefore[/tex] The distance between the point R and S is √145 or approximate 12.04 units.

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