Question

What is the distance between the following points?

Answer 1

Point are

• (2,-3)
• (8,-9)

Using distance formula

$\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\\ \sf\longmapsto \sqrt{(8-2)^2+(-9+3)^2}$

$\\ \sf\longmapsto \sqrt{6^2+(-6)^2}$

$\\ \sf\longmapsto \sqrt{36+36}$

$\\ \sf\longmapsto \sqrt{72}$

$\\ \sf\longmapsto 8.2units$

Answer 2

Given Points

• ⇛ 2 , -3 ( x = 2 and y = -3 )

• ⇛ 8 , -9 ( x= 8 and y = -9 )

Using Formula

$\begin{gathered} {\underline{\boxed{ \rm {\red{ Distance \: = \: \sqrt{(x_2 \: - \: x_1) ^{2} \: + \:(y_2 \: - \: y_1)} }}}}}\end{gathered}$

Substuting the values

$\bf \longrightarrow \:Distance \: = \: \sqrt{ \bigg(8 \: - \: 2 \bigg) ^{2} \: + \: \bigg( - 9 \: - \: (- 3) \bigg)^{2} }$

$\bf \longrightarrow \:Distance \: = \: \sqrt{ \bigg(8 \: - \: 2 \bigg) ^{2} \: + \: \bigg( - 9 \: + \: 3 \bigg)^{2} }$

$\bf \longrightarrow \:Distance \: = \: \sqrt{ (6 ) ^{2} \: + \:( - 6 )^{2} }$

$\bf \longrightarrow \:Distance \: = \: \sqrt{ (36 ) \: + \:( 36 ) }$

$\bf \longrightarrow \:Distance \: = \: \sqrt{72}$

$\bf \longrightarrow \:Distance \: = \: 8.485281$

Approximate distance = 8.4

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Hence , the distance between 2 points is

8.4 units