Distance Between Two Points 3

Question 1 of 6

Find the distance between each pair of points.

Round your answer to the nearest tenth.

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

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 (

$A($ $- 4$ $-4$

,

$,$ $4$ $4$

) = A (

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

,

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

)

$)$

B (

$B($ $1$ $1$

,

$,$ $3$ $3$

) = 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
	$=$ $=$	$\sqrt{(\color{#9202AA}{1}-\color{#9202AA}{(-4)})^2+(\color{#00880A}{3}-\color{#00880A}{4})^2}$	Plug in the coordinates
	$=$ $=$	$\sqrt{5^{2} + {(- 1)}^{2}}$ $sqrt(5^2 + (-1)^2)$	Simplify
	$=$ $=$	$\sqrt{25 + 1}$ $sqrt(25 + 1)$
	$=$ $=$	$\sqrt{26}$ $sqrt(26)$	Take the square root
	$=$ $=$	$5.099019514$ $5.099019514$
	$=$ $=$	$5.1$ $5.1$ units	Round to the nearest tenth

Distance = 5.1 units

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

Question 2 of 6

Find the distance between each pair of points.

Round your answer to the nearest tenth.

$Distance =$ $\text(Distance) =$ (3.6) $units$ $\text(units)$

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 (

$A($ $1$ $1$

,

$,$ $1$ $1$

) = A (

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

,

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

)

$)$

B (

$B($ $4$ $4$

,

$,$ $3$ $3$

) = 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
	$=$ $=$	$\sqrt{(\color{#9202AA}{4}-\color{#9202AA}{1})^2+(\color{#00880A}{3}-\color{#00880A}{1})^2}$	Plug in the coordinates
	$=$ $=$	$\sqrt{3^{2} + 2^{2}}$ $sqrt(3^2 + 2^2)$	Simplify
	$=$ $=$	$\sqrt{9 + 4}$ $sqrt(9 + 4)$
	$=$ $=$	$\sqrt{13}$ $sqrt(13)$	Take the square root
	$=$ $=$	$3.605551275$ $3.605551275$
	$=$ $=$	$3.6$ $3.6$ units	Round to the nearest tenth

Distance = 3.6 units

$\text(Distance) =3.6 \text(units)$

Question 3 of 6

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (6.40)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 (- 3, 5) = A (x_{1}, y_{1})

$A(color(darkviolet)(-3),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

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

$B(color(darkviolet)(2),color(forestgreen)(1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

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
	$=$ $=$	$\sqrt{{(2 - (- 3))}^{2} + {(1 - 5)}^{2}}$ $sqrt((color(darkviolet)(2-(-3)))^2+(color(forestgreen)(1-5))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{5^{2} + {(- 4)}^{2}}$ $sqrt(5^2 + (-4)^2)$	Simplify
	$=$ $=$	$\sqrt{25 + 16}$ $sqrt(25 + 16)$
	$=$ $=$	$\sqrt{41}$ $sqrt(41)$	Take the square root
	$=$ $=$	$6.403124$ $6.403124$
	$=$ $=$	$6.40$ $6.40$	Rounded to $2$ $2$ decimal places

Distance

= 6.40 units

$=6.40 \ text(units)$

Question 4 of 6

Find the distance between $A (1.5, 1)$ $A(1.5,1)$ and $B (4, - 2)$ $B(4,-2)$

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (3.91)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 (1.5, 1) = A (x_{1}, y_{1})

$A(color(darkviolet)(1.5),color(forestgreen)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

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
	$=$ $=$	$\sqrt{({1.5 - 4}^{2} + {(1 - (- 2))}^{2})}$ $sqrt((color(darkviolet)(1.5-4)^2+(color(forestgreen)(1-(-2)))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{{(- 2.5)}^{2} + 3^{2}}$ $sqrt((-2.5)^2 + 3^2)$	Simplify
	$=$ $=$	$\sqrt{6.25 + 9}$ $sqrt(6.25 + 9)$
	$=$ $=$	$\sqrt{15.25}$ $sqrt(15.25)$	Take the square root
	$=$ $=$	$3.905125$ $3.905125$
	$=$ $=$	$3.91$ $3.91$	Rounded to $2$ $2$ decimal places

Distance

= 3.91 units

$=3.91 \ text(units)$

Question 5 of 6

Find the distance between $A (- 1, 5)$ $A(-1,5)$ and $B (0, - 3)$ $B(0,-3)$

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (8.06)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, 5) = A (x_{1}, y_{1})

$A(color(darkviolet)(-1),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (0, - 3) = B (x_{2}, y_{2})

$B(color(darkviolet)(0),color(forestgreen)(-3))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

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
	$=$ $=$	$\sqrt{{(- 1 - 0)}^{2} + {(5 - (- 3))}^{2}}$ $sqrt((color(darkviolet)(-1-0))^2+(color(forestgreen)(5-(-3)))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{{(- 1)}^{2} + 8^{2}}$ $sqrt((-1)^2 + 8^2)$	Simplify
	$=$ $=$	$\sqrt{1 + 64}$ $sqrt(1 + 64)$
	$=$ $=$	$\sqrt{65}$ $sqrt(65)$	Take the square root
	$=$ $=$	`8.062258
	$=$ $=$	$8.06$ $8.06$	Rounded to $2$ $2$ decimal places

Distance

= 8.06 units

$=8.06 \ text(units)$

Question 6 of 6

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

Round your answer to

2

$2$ decimal places

Distance $=$ $=$ (5)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 (2, - 1) = B (x_{2}, y_{2})

$B(color(darkviolet)(2),color(forestgreen)(-1))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

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
	$=$ $=$	$\sqrt{{(- 2 - 2)}^{2} + {(2 - (- 1))}^{2}}$ $sqrt((color(darkviolet)(-2-2))^2+(color(forestgreen)(2-(-1)))^2)$	Plug in the coordinates
	$=$ $=$	$\sqrt{{(- 4)}^{2} + 3^{2}}$ $sqrt((-4)^2 + 3^2)$	Simplify
	$=$ $=$	$\sqrt{16 + 9}$ $sqrt(16 + 9)$
	$=$ $=$	$\sqrt{25}$ $sqrt(25)$	Take the square root
	$=$ $=$	$5.00$ $5.00$
	$=$ $=$	$5$ $5$	Rounded to $2$ $2$ decimal places

Distance

= 5 units

$=5 \ text(units)$

Distance Between Two Points 3

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Quiz summary

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1. Question

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2. Question

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