Answered

IDNStudy.com, ang iyong destinasyon para sa mga sagot ng eksperto. Makakuha ng mga kumpletong sagot sa lahat ng iyong mga tanong mula sa aming network ng mga eksperto.

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 )

​

Sagot :

UK2019idn

✏️DISTANCES

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[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)

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[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]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[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]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#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.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnLearning

Ang iyong aktibong pakikilahok ay mahalaga sa amin. Magpatuloy sa pagtatanong at pagbahagi ng iyong nalalaman. Sama-sama tayong lumikha ng isang komunidad ng karunungan. IDNStudy.com ang iyong mapagkakatiwalaang kasama para sa lahat ng iyong mga katanungan. Bisitahin kami palagi.