Distance Between Two Points 2
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Question 1 of 7
1. Question
Find the distance between `A(0,-1)` and `B(5,6)`
Round your answer to two decimal places- `\text(Distance) =` (8.60)`\text(units)`
Hint
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Distance Formula
$$d=\sqrt{(\color{#7d02aa}{x_2}-\color{#7d02aa}{x_1})^2+(\color{#00880a}{y_2}-\color{#00880a}{y_1})^2}$$First, label the given coordinates`A(``0``,``-1``) = A(``x_1``,``y_1``)``B(``5``,``6``) = B(``x_2``,``y_2``)`Solve using the Distance Formula`\text(Distance)` `=` $$\sqrt{(\color{#7d02aa}{x_2}-\color{#7d02aa}{x_1})^2+(\color{#00880a}{y_2}-\color{#00880a}{y_1})^2}$$ Distance Formula `=` $$\sqrt{(\color{#7d02aa}{5}-\color{#7d02aa}{6})^2+(\color{#00880a}{4}-\color{#00880a}{(-1)})^2}$$ Plug in the coordinates `=` `sqrt(5^2 + 7^2)` Simplify `=` `sqrt(25 + 49)` `=` `sqrt(74)` Take the square root `=` `8.602325267` `=` `8.60` Round two two decimal places `\text(Distance) =8.60 \text(units)` -
Question 2 of 7
2. Question
Find the distance between each pair of points.
Round your answer to the nearest tenth.- `\text(Distance) =` (4.5)`\text(units)`
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Distance Formula
$$d=\sqrt{(\color{#9202AA}{x_2}-\color{#9202AA}{x_1})^2+(\color{#00880A}{y_2}-\color{#00880A}{y_1})^2}$$First, label the given coordinates`A(``-2``,``3``) = A(``x_1``,``y_1``)``B(``0``,``-1``) = B(``x_2``,``y_2``)`Solve using the Distance Formula`\text(Distance)` `=` $$\sqrt{(\color{#9202AA}{x_2}-\color{#9202AA}{x_1})^2+(\color{#00880A}{y_2}-\color{#00880A}{y_1})^2}$$ Distance Formula `=` $$\sqrt{(\color{#9202AA}{0}-\color{#9202AA}{(-2)})^2+(\color{#00880A}{-1}-\color{#00880A}{(-3)})^2}$$ Plug in the coordinates `=` `sqrt(2^2 + (-4)^2)` Simplify `=` `sqrt(4 + 16)` `=` `sqrt(20)` Take the square root `=` `4.472135955` `=` `4.5` units Round to the nearest tenth `\text(Distance) =4.5 \text(units)` -
Question 3 of 7
3. Question
Find the distance between `A(0,1)` and `B(1,3)`
Round your answer to `2` decimal places- Distance`=` (2.24)units
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Distance Formula
`d=sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)`First, label the given coordinates`A(color(darkviolet)(0),color(forestgreen)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(1),color(forestgreen)(3))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Distance FormulaDistance `=` `sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)` Distance Formula `=` `sqrt((color(darkviolet)(1-0))^2+(color(forestgreen)(3-1))^2)` Plug in the coordinates `=` `sqrt(1^2 + 2^2)` Simplify `=` `sqrt(1 + 4)` `=` `sqrt(5)` Take the square root `=` `2.236067` `=` `2.24` Rounded to `2` decimal places Distance`=2.24 \ text(units)` -
Question 4 of 7
4. Question
Find the distance between `A(-2,-2)` and `B(4,-1)`
Round your answer to `2` decimal places- Distance`=` (6.08)units
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Distance Formula
`d=sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)`First, label the given coordinates`A(color(darkviolet)(-2),color(forestgreen)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(4),color(forestgreen)(-1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Distance FormulaDistance `=` `sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)` Distance Formula `=` `sqrt((color(darkviolet)(4-(-2)))^2+(color(forestgreen)(-1-(-2)))^2)` Plug in the coordinates `=` `sqrt(6^2 + 1^2)` Simplify `=` `sqrt(36 + 1)` `=` `sqrt(37)` Take the square root `=` `6.08276` `=` `6.08` Rounded to `2` decimal places Distance`=6.08 \ text(units)` -
Question 5 of 7
5. Question
Find the distance between `A(-1,6)` and `B(-3,1)`
Round your answer to `2` decimal places- Distance`=` (5.39)units
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Distance Formula
`d=sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)`First, label the given coordinates`A(color(darkviolet)(-1),color(forestgreen)(6))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(-3),color(forestgreen)(1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Distance FormulaDistance `=` `sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)` Distance Formula `=` `sqrt((color(darkviolet)(-1-(-3)))^2+(color(forestgreen)(6-1))^2)` Plug in the coordinates `=` `sqrt(2^2 + 5^2)` Simplify `=` `sqrt(4 + 25)` `=` `sqrt(41)` Take the square root `=` `5.385164` `=` `5.39` Rounded to `2` decimal places Distance`=5.39 \ text(units)` -
Question 6 of 7
6. Question
Find the distance between `A(5,4)` and `B(-4,-2)`
Round your answer to `2` decimal places- Distance`=` (10.82)units
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Distance Formula
`d=sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)`First, label the given coordinates`A(color(darkviolet)(5),color(forestgreen)(4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(-4),color(forestgreen)(-2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Distance FormulaDistance `=` `sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)` Distance Formula `=` `sqrt((color(darkviolet)(5-(-4)))^2+(color(forestgreen)(4-(-2))^2)` Plug in the coordinates `=` `sqrt(9^2 + 6^2)` Simplify `=` `sqrt(81+ 36)` `=` `sqrt(117)` Take the square root `=` `10.816654` `=` `10.82` Rounded to `2` decimal places Distance`=10.82 \ text(units)` -
Question 7 of 7
7. Question
Find the distance between `A(-1,-4)` and `B(5,-2)`
Round your answer to `2` decimal places- Distance`=` (6.32)units
Correct
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Distance Formula
`d=sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)`First, label the given coordinates`A(color(darkviolet)(-1),color(forestgreen)(-4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(5),color(forestgreen)(-2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Distance FormulaDistance `=` `sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)` Distance Formula `=` `sqrt((color(darkviolet)(-1-5))^2+(color(forestgreen)(-4-(-2)))^2)` Plug in the coordinates `=` `sqrt((-6)^2 + (-2)^2)` Simplify `=` `sqrt(36 + 4)` `=` `sqrt(40)` Take the square root `=` `6.324555` `=` `6.32` Rounded to `2` decimal places Distance`=6.32 \ text(units)`