Distance Between Two Points 1
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Question 1 of 7
1. Question
Find the distance between `A(6,3)` and `B(2,6)`
- Distance`=` (5)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)(6),color(forestgreen)(3))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(2),color(forestgreen)(6))=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)(2-6))^2+(color(forestgreen)(6-3))^2)` Plug in the coordinates `=` `sqrt((-4)^2 + 3^2)` Simplify `=` `sqrt(16 + 9)` `=` `sqrt(25)` Take the square root `=` `5` Distance`=5 \ text(units)` -
Question 2 of 7
2. Question
Find the distance between `A(-4,3)` and `B(3,1)`
Round your answer to `2` decimal places- Distance`=` (7.28)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)(-4),color(forestgreen)(3))=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)(3-(-4)))^2+(color(forestgreen)(1-3))^2)` Plug in the coordinates `=` `sqrt(7^2 + (-2)^2)` Simplify `=` `sqrt(49+4)` `=` `sqrt(53)` Take the square root `=` `7.2801098` `=` `7.28` Rounded to `2` decimal places Distance`=7.28 \ text(units)` -
Question 3 of 7
3. Question
Find the distance between `A(-2,4)` and `B(1,1)`
Round your answer to `2` decimal places- Distance`=` (4.24)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)(-2),color(forestgreen)(4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(1),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)(-2-1))^2+(color(forestgreen)(4-1))^2)` Plug in the coordinates `=` `sqrt((-3)^2 + 3^2)` Simplify `=` `sqrt(9 + 9)` `=` `sqrt(18)` Take the square root `=` `4.242641` `=` `4.24` Rounded to `2` decimal places Distance`=4.24 \ text(units)` -
Question 4 of 7
4. Question
Find the distance between `A(-1,2)` and `B(5,4)`
Round your answer to two decimal places- `\text(Distance) =` (6.32)`\text(units)`
Hint
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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(``-1``,``2``) = A(``x_1``,``y_1``)``B(``5``,``4``) = 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 `=` $$\sqrt{(\color{#9202AA}{5}-\color{#9202AA}{(-1)})^2+(\color{#00880A}{4}-\color{#00880A}{(2)})^2}$$ Plug in the coordinates `=` `sqrt(6^2 + 2^2)` Simplify `=` `sqrt(36 + 4)` `=` `sqrt(40)` Take the square root `=` `6.32455532` `=` `6.32` units Round to two decimal places `\text(Distance) =6.32 \text(units)` -
Question 5 of 7
5. Question
Find the distance between `A(1,-2)` and `B(5,-3)`
Round your answer to `2` decimal places- Distance`=` (4.12)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)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(5),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)(1-5))^2+(color(forestgreen)(-2-(-3)))^2)` Plug in the coordinates `=` `sqrt((-4)^2 + 1^2)` Simplify `=` `sqrt(16 + 1)` `=` `sqrt(17)` Take the square root `=` `4.123106` `=` `4.12` Rounded to `2` decimal places Distance`=4.12 \ text(units)` -
Question 6 of 7
6. Question
Find the distance between `A(-1,-2)` and `B(2,-4)`
Round your answer to `2` decimal places- Distance`=` (3.61)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)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(2),color(forestgreen)(-4))=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)(-1-2))^2+(color(forestgreen)(-2-(-4)))^2)` Plug in the coordinates `=` `sqrt((-3)^2 + 2^2)` Simplify `=` `sqrt(9+4)` `=` `sqrt(13)` Take the square root `=` `3.605551` `=` `3.61` Rounded to `2` decimal places Distance`=6.40 \ text(units)` -
Question 7 of 7
7. Question
Find the distance between `A(-1,-8)` and `B(3,-3)`
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)(-1),color(forestgreen)(-8))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(3),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)(-1-3))^2+(color(forestgreen)(-8-(-3)))^2)` Plug in the coordinates `=` `sqrt((-4)^2 + (-5)^2)` Simplify `=` `sqrt(16+25)` `=` `sqrt(41)` Take the square root `=` `6.403124` `=` `6.40` Rounded to `2` decimal places Distance`=6.40 \ text(units)`
Quizzes
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Gradient of a Line 1
- Gradient of a Line 2
- Gradient Intercept Form: Graph an Equation 1
- Gradient Intercept Form: Graph an Equation 2
- Gradient Intercept Form: Write an Equation 1
- Determine if a Point Lies on a Line
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Convert Between General Form and Gradient Intercept Form 1
- Convert Between General Form and Gradient Intercept Form 2
- Point Gradient and Two Point Formula 1
- Point Gradient and Two Point Formula 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2