Distance Between Two Points

Analytic Geometry

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Question 1 of 5

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

Help Video

Correct

Nice Job!

Incorrect

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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 5

2. Question

Find the distance between each pair of points.

Round your answer to the nearest tenth.

`\text(Distance) =` (5.1)`\text(units)`

Correct

Well Done!

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(``-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 3 of 5

3. Question

Find the distance between each pair of points.

Round your answer to the nearest tenth.

`\text(Distance) =` (4.5)`\text(units)`

Correct

Keep Going!

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(``-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 4 of 5

4. 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 5 of 5

5. 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

Help Video

Correct

Great Work!

Incorrect

Help Video

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)`

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