Distance Between Two Points 2

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Geometry

Analytic Geometry

Distance Between Two Points

Distance Between Two Points 2

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Question 1 of 7

Find the distance between

$A(0,-1)$ and

$B(5,6)$

Round your answer to two decimal places

$\text(Distance) =$ (8.60) $\text(units)$

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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

Find the distance between each pair of points.

Round your answer to the nearest tenth.

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

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 3 of 7

Find the distance between $A(0,1)$ and $B(1,3)$

Round your answer to

$2$ decimal places

Distance $=$ (2.24)units

Question 4 of 7

Find the distance between $A(-2,-2)$ and $B(4,-1)$

Round your answer to

$2$ decimal places

Distance $=$ (6.08)units

Question 5 of 7

Find the distance between $A(-1,6)$ and $B(-3,1)$

Round your answer to

$2$ decimal places

Distance $=$ (5.39)units

Question 6 of 7

Find the distance between $A(5,4)$ and $B(-4,-2)$

Round your answer to

$2$ decimal places

Distance $=$ (10.82)units

Question 7 of 7

Find the distance between $A(-1,-4)$ and $B(5,-2)$

Round your answer to

$2$ decimal places

Distance $=$ (6.32)units

Distance Between Two Points 2

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Quiz summary

Information

1. Question

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Distance Formula

2. Question

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Distance Formula

3. Question

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Distance Formula

4. Question

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Distance Formula

5. Question

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Distance Formula

6. Question

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Distance Formula

7. Question

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Distance Formula

Quizzes

Distance	$=$	$sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)$	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