Distance Between Two Points 1

Topics

Geometry

Analytic Geometry

Distance Between Two Points

Distance Between Two Points 1

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Question 1 of 7

Find the distance between $A (6, 3)$ $A(6,3)$ and $B (2, 6)$ $B(2,6)$

Distance $=$ $=$ (5)units

Question 2 of 7

Find the distance between $A(-4,3)$ and $B(3,1)$

Round your answer to

$2$ decimal places

Distance $=$ (7.28)units

Question 3 of 7

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

Round your answer to

$2$ decimal places

Distance $=$ (4.24)units

Question 4 of 7

Find the distance between

$A(-1,2)$ and

$B(5,4)$

Round your answer to two decimal places

$\text(Distance) =$ (6.32) $\text(units)$

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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

$A($ $-1$

$,$ $2$

$) = A($ $x_1$

$,$ $y_1$

$)$

$B($ $5$

$,$ $4$

$) = B($ $x_2$

$,$ $y_2$

$)$

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

Find the distance between $A(1,-2)$ and $B(5,-3)$

Round your answer to

$2$ decimal places

Distance $=$ (4.12)units

Question 6 of 7

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

Round your answer to

$2$ decimal places

Distance $=$ (3.61)units

Question 7 of 7

Find the distance between $A(-1,-8)$ and $B(3,-3)$

Round your answer to

$2$ decimal places

Distance $=$ (6.40)units

Distance Between Two Points 1

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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

Hint

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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	$=$ $=$	$\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ $sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)$	Distance Formula
	$=$ $=$	$\sqrt{{(2 - 6)}^{2} + {(6 - 3)}^{2}}$ $sqrt((color(darkviolet)(2-6))^2+(color(forestgreen)(6-3))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{{(- 4)}^{2} + 3^{2}}$ $sqrt((-4)^2 + 3^2)$	Simplify
	$=$ $=$	$\sqrt{16 + 9}$ $sqrt(16 + 9)$
	$=$	$sqrt(25)$	Take the square root
	$=$	$5$

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