Distance Between Two Points 2

Years

Year 9

Coordinate 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)

$A(0,-1)$ and

B (5, 6)

$B(5,6)$

Round your answer to two decimal places

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

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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

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

Hint

Nice Job!

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	$=$ $=$	$\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ $sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)$	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
	$=$	$sqrt(1 + 4)$
	$=$	$sqrt(5)$	Take the square root
	$=$	$2.236067$
	$=$	$2.24$	Rounded to $2$ decimal places

Distance	$=$	$sqrt((color(darkviolet)(x_2-x_1))^2+(color(forestgreen)(y_2-y_1))^2)$	Distance Formula
	$=$	$sqrt((color(darkviolet)(4-(-2)))^2+(color(forestgreen)(-1-(-2)))^2)$	Plug in the coordinates
	$=$	$sqrt(6^2 + 1^2)$	Simplify
	$=$	$sqrt(36 + 1)$
	$=$	$sqrt(37)$	Take the square root
	$=$	$6.08276$
	$=$	$6.08$	Rounded to $2$ decimal places