Distance Between Two Points 2

Question 1 of 7

Find the distance between

A (0, - 1)

$A(0,-1)$ and

B (5, 6)

$B(5,6)$

Round your answer to two decimal places

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

Incorrect

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Distance Formula

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}

$d=\sqrt{(\color{#7d02aa}{x_2}-\color{#7d02aa}{x_1})^2+(\color{#00880a}{y_2}-\color{#00880a}{y_1})^2}$

First, label the given coordinates

A (

$A($ $0$ $0$

,

$,$ $- 1$ $-1$

) = A (

$) = A($ $x_{1}$ $x_1$

,

$,$ $y_{1}$ $y_1$

)

$)$

B (

$B($ $5$ $5$

,

$,$ $6$ $6$

) = B (

$) = B($ $x_{2}$ $x_2$

,

$,$ $y_{2}$ $y_2$

)

$)$

Solve using the Distance Formula

$Distance$ $\text(Distance)$	$=$ $=$	$\sqrt{(\color{#7d02aa}{x_2}-\color{#7d02aa}{x_1})^2+(\color{#00880a}{y_2}-\color{#00880a}{y_1})^2}$	Distance Formula
	$=$ $=$	$\sqrt{(\color{#7d02aa}{5}-\color{#7d02aa}{6})^2+(\color{#00880a}{4}-\color{#00880a}{(-1)})^2}$	Plug in the coordinates
	$=$ $=$	$\sqrt{5^{2} + 7^{2}}$ $sqrt(5^2 + 7^2)$	Simplify
	$=$ $=$	$\sqrt{25 + 49}$ $sqrt(25 + 49)$
	$=$ $=$	$\sqrt{74}$ $sqrt(74)$	Take the square root
	$=$ $=$	$8.602325267$ $8.602325267$
	$=$ $=$	$8.60$ $8.60$	Round two two decimal places

Distance = 8.60 units

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

Question 2 of 7

Find the distance between each pair of points.

Round your answer to the nearest tenth.

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

Incorrect

Distance Formula

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}

$d=\sqrt{(\color{#9202AA}{x_2}-\color{#9202AA}{x_1})^2+(\color{#00880A}{y_2}-\color{#00880A}{y_1})^2}$

First, label the given coordinates

A (

$A($ $- 2$ $-2$

,

$,$ $3$ $3$

) = A (

$) = A($ $x_{1}$ $x_1$

,

$,$ $y_{1}$ $y_1$

)

$)$

B (

$B($ $0$ $0$

,

$,$ $- 1$ $-1$

) = B (

$) = B($ $x_{2}$ $x_2$

,

$,$ $y_{2}$ $y_2$

)

$)$

Solve using the Distance Formula

$Distance$ $\text(Distance)$	$=$ $=$	$\sqrt{(\color{#9202AA}{x_2}-\color{#9202AA}{x_1})^2+(\color{#00880A}{y_2}-\color{#00880A}{y_1})^2}$	Distance Formula
	$=$ $=$	$\sqrt{(\color{#9202AA}{0}-\color{#9202AA}{(-2)})^2+(\color{#00880A}{-1}-\color{#00880A}{(-3)})^2}$	Plug in the coordinates
	$=$ $=$	$\sqrt{2^{2} + {(- 4)}^{2}}$ $sqrt(2^2 + (-4)^2)$	Simplify
	$=$ $=$	$\sqrt{4 + 16}$ $sqrt(4 + 16)$
	$=$ $=$	$\sqrt{20}$ $sqrt(20)$	Take the square root
	$=$ $=$	$4.472135955$ $4.472135955$
	$=$ $=$	$4.5$ $4.5$ units	Round to the nearest tenth

Distance = 4.5 units

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

Question 3 of 7

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (2.24)units

Incorrect

Distance Formula

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

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

First, label the given coordinates

A (0, 1) = A (x_{1}, y_{1})

$A(color(darkviolet)(0),color(forestgreen)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (1, 3) = B (x_{2}, y_{2})

$B(color(darkviolet)(1),color(forestgreen)(3))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Distance Formula

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
	$=$ $=$	$\sqrt{{(1 - 0)}^{2} + {(3 - 1)}^{2}}$ $sqrt((color(darkviolet)(1-0))^2+(color(forestgreen)(3-1))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{1^{2} + 2^{2}}$ $sqrt(1^2 + 2^2)$	Simplify
	$=$ $=$	$\sqrt{1 + 4}$ $sqrt(1 + 4)$
	$=$ $=$	$\sqrt{5}$ $sqrt(5)$	Take the square root
	$=$ $=$	$2.236067$ $2.236067$
	$=$ $=$	$2.24$ $2.24$	Rounded to $2$ $2$ decimal places

Distance

= 2.24 units

$=2.24 \ text(units)$

Question 4 of 7

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (6.08)units

Incorrect

Distance Formula

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

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

First, label the given coordinates

A (- 2, - 2) = A (x_{1}, y_{1})

$A(color(darkviolet)(-2),color(forestgreen)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (4, - 1) = B (x_{2}, y_{2})

$B(color(darkviolet)(4),color(forestgreen)(-1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Distance Formula

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
	$=$ $=$	$\sqrt{{(4 - (- 2))}^{2} + {(- 1 - (- 2))}^{2}}$ $sqrt((color(darkviolet)(4-(-2)))^2+(color(forestgreen)(-1-(-2)))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{6^{2} + 1^{2}}$ $sqrt(6^2 + 1^2)$	Simplify
	$=$ $=$	$\sqrt{36 + 1}$ $sqrt(36 + 1)$
	$=$ $=$	$\sqrt{37}$ $sqrt(37)$	Take the square root
	$=$ $=$	$6.08276$ $6.08276$
	$=$ $=$	$6.08$ $6.08$	Rounded to $2$ $2$ decimal places

Distance

= 6.08 units

$=6.08 \ text(units)$

Question 5 of 7

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (5.39)units

Incorrect

Distance Formula

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

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

First, label the given coordinates

A (- 1, 6) = A (x_{1}, y_{1})

$A(color(darkviolet)(-1),color(forestgreen)(6))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (- 3, 1) = B (x_{2}, y_{2})

$B(color(darkviolet)(-3),color(forestgreen)(1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Distance Formula

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
	$=$ $=$	$\sqrt{{(- 1 - (- 3))}^{2} + {(6 - 1)}^{2}}$ $sqrt((color(darkviolet)(-1-(-3)))^2+(color(forestgreen)(6-1))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{2^{2} + 5^{2}}$ $sqrt(2^2 + 5^2)$	Simplify
	$=$ $=$	$\sqrt{4 + 25}$ $sqrt(4 + 25)$
	$=$ $=$	$\sqrt{41}$ $sqrt(41)$	Take the square root
	$=$ $=$	$5.385164$ $5.385164$
	$=$ $=$	$5.39$ $5.39$	Rounded to $2$ $2$ decimal places

Distance

= 5.39 units

$=5.39 \ text(units)$

Question 6 of 7

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (10.82)units

Incorrect

Distance Formula

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

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

First, label the given coordinates

A (5, 4) = A (x_{1}, y_{1})

$A(color(darkviolet)(5),color(forestgreen)(4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (- 4, - 2) = B (x_{2}, y_{2})

$B(color(darkviolet)(-4),color(forestgreen)(-2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Distance Formula

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
	$=$ $=$	$\sqrt{{(5 - (- 4))}^{2} + ({4 - (- 2)}^{2})}$ $sqrt((color(darkviolet)(5-(-4)))^2+(color(forestgreen)(4-(-2))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{9^{2} + 6^{2}}$ $sqrt(9^2 + 6^2)$	Simplify
	$=$ $=$	$\sqrt{81 + 36}$ $sqrt(81+ 36)$
	$=$ $=$	$\sqrt{117}$ $sqrt(117)$	Take the square root
	$=$ $=$	$10.816654$ $10.816654$
	$=$ $=$	$10.82$ $10.82$	Rounded to $2$ $2$ decimal places

Distance

= 10.82 units

$=10.82 \ text(units)$

Question 7 of 7

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (6.32)units

Incorrect

Distance Formula

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

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

First, label the given coordinates

A (- 1, - 4) = A (x_{1}, y_{1})

$A(color(darkviolet)(-1),color(forestgreen)(-4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (5, - 2) = B (x_{2}, y_{2})

$B(color(darkviolet)(5),color(forestgreen)(-2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Distance Formula

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
	$=$ $=$	$\sqrt{{(- 1 - 5)}^{2} + {(- 4 - (- 2))}^{2}}$ $sqrt((color(darkviolet)(-1-5))^2+(color(forestgreen)(-4-(-2)))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{{(- 6)}^{2} + {(- 2)}^{2}}$ $sqrt((-6)^2 + (-2)^2)$	Simplify
	$=$ $=$	$\sqrt{36 + 4}$ $sqrt(36 + 4)$
	$=$ $=$	$\sqrt{40}$ $sqrt(40)$	Take the square root
	$=$ $=$	$6.324555$ $6.324555$
	$=$ $=$	$6.32$ $6.32$	Rounded to $2$ $2$ decimal places

Distance

= 6.32 units

$=6.32 \ text(units)$

Distance Between Two Points 2

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