Distance Between Two Points 3
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Question 1 of 6
1. Question
Find the distance between each pair of points.
Round your answer to the nearest tenth.- `\text(Distance) =` (5.1)`\text(units)`
Correct
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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(``-4``,``4``) = A(``x_1``,``y_1``)``B(``1``,``3``) = 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 `=` $$\sqrt{(\color{#9202AA}{1}-\color{#9202AA}{(-4)})^2+(\color{#00880A}{3}-\color{#00880A}{4})^2}$$ Plug in the coordinates `=` `sqrt(5^2 + (-1)^2)` Simplify `=` `sqrt(25 + 1)` `=` `sqrt(26)` Take the square root `=` `5.099019514` `=` `5.1` units Round to the nearest tenth `\text(Distance) =5.1 \text(units)` -
Question 2 of 6
2. Question
Find the distance between each pair of points.
Round your answer to the nearest tenth.- `\text(Distance) =` (3.6)`\text(units)`
Correct
Correct!
Incorrect
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(``1``,``1``) = A(``x_1``,``y_1``)``B(``4``,``3``) = 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 `=` $$\sqrt{(\color{#9202AA}{4}-\color{#9202AA}{1})^2+(\color{#00880A}{3}-\color{#00880A}{1})^2}$$ Plug in the coordinates `=` `sqrt(3^2 + 2^2)` Simplify `=` `sqrt(9 + 4)` `=` `sqrt(13)` Take the square root `=` `3.605551275` `=` `3.6` units Round to the nearest tenth `\text(Distance) =3.6 \text(units)` -
Question 3 of 6
3. Question
Find the distance between `A(-3,5)` and `B(2,1)`
Round your answer to `2` decimal places- Distance`=` (6.40)units
Correct
Keep Going!
Incorrect
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)(-3),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(2),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)(2-(-3)))^2+(color(forestgreen)(1-5))^2)` Plug in the coordinates `=` `sqrt(5^2 + (-4)^2)` Simplify `=` `sqrt(25 + 16)` `=` `sqrt(41)` Take the square root `=` `6.403124` `=` `6.40` Rounded to `2` decimal places Distance`=6.40 \ text(units)` -
Question 4 of 6
4. Question
Find the distance between `A(1.5,1)` and `B(4,-2)`
Round your answer to `2` decimal places- Distance`=` (3.91)units
Correct
Keep Going!
Incorrect
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)(1.5),color(forestgreen)(1))=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)(1.5-4)^2+(color(forestgreen)(1-(-2)))^2)` Plug in the coordinates `=` `sqrt((-2.5)^2 + 3^2)` Simplify `=` `sqrt(6.25 + 9)` `=` `sqrt(15.25)` Take the square root `=` `3.905125` `=` `3.91` Rounded to `2` decimal places Distance`=3.91 \ text(units)` -
Question 5 of 6
5. Question
Find the distance between `A(-1,5)` and `B(0,-3)`
Round your answer to `2` decimal places- Distance`=` (8.06)units
Correct
Keep Going!
Incorrect
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)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(0),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)(5-(-3)))^2)` Plug in the coordinates `=` `sqrt((-1)^2 + 8^2)` Simplify `=` `sqrt(1 + 64)` `=` `sqrt(65)` Take the square root `=` `8.062258 `=` `8.06` Rounded to `2` decimal places Distance`=8.06 \ text(units)` -
Question 6 of 6
6. Question
Find the distance between `A(-2,2)` and `B(2,-1)`
Round your answer to `2` decimal places- Distance`=` (5)units
Correct
Keep Going!
Incorrect
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)(2),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)(-2-2))^2+(color(forestgreen)(2-(-1)))^2)` Plug in the coordinates `=` `sqrt((-4)^2 + 3^2)` Simplify `=` `sqrt(16 + 9)` `=` `sqrt(25)` Take the square root `=` `5.00` `=` `5` Rounded to `2` decimal places Distance`=5 \ text(units)`