Question

find the distance between the points (6,4) and (8,9)​

Answer 1

Answer:

${\rm\sqrt{29} \: units }$

Explanation:

Let the given points,

• A(6, 4)
• B(8, 9)

Using distance formula :

$\rm \longrightarrow \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} }$

Where,

• $\rm x_1 \: and \: y_1$ denotes the coordinates of point A i.e., 6 and 8 respectively.
• Similarly, $\rm x_2 \: and \: y_2$ is 4 and 9 respectively.

Substituting the given coordinates :

$\rm \longrightarrow \sqrt{ {(8 - 6)}^{2} + {(9 - 4)}^{2} }$

$\rm \longrightarrow \sqrt{ {(2)}^{2} + {(5)}^{2} }$

$\rm \longrightarrow \sqrt{4 + 25 }$

$\rm \longrightarrow \sqrt{29 }$

$\underline{ \rm \therefore \: Distance \: between \: A \: and \: B \: is \: \sqrt{29} \: units }$

_____________________

Note:

Distance formula,

• $\rm \longrightarrow \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} }$

Where,

• $\rm x_1 \: and \: y_1$ denotes the coordinates of the first point.
• $\rm x_2 \: and \: y_2$ denotes the coordinates of the second point.

Answer 2

Aɴsᴡᴇʀ:

${\rm\sqrt{29} \: units }$

Exᴘʟᴀɴᴀᴛɪᴏɴ:

Let the given points,

A(6, 4)

B(8, 9)

Using distance formula :

$\rm \longrightarrow \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} }$

Where,

$\rm x_1 \: and \: y_1$ denotes the coordinates of point A i.e., 6 and 8 respectively.

Similarly, $\rm x_2 \: and \: y_2$ is 4 and 9 respectively.

Substituting the given coordinates :

$\rm \longrightarrow \sqrt{ {(8 - 6)}^{2} + {(9 - 4)}^{2} }$

$\rm \longrightarrow \sqrt{ {(2)}^{2} + {(5)}^{2} }$

$\rm \longrightarrow \sqrt{4 + 25 }$

$\rm \longrightarrow \sqrt{29 }$

$\underline{ \rm \therefore \: Distance \: between \: A \: and \: B \: is \: \sqrt{29} \: units }$

_____________________

Note:

Distance formula,

$\rm \longrightarrow \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} }$

Where,

$\rm x_1 \: and \: y_1$ denotes the coordinates of the first point.

$\rm x_2 \: and \: y_2$ denotes the coordinates of the second point.

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