Question

find the distance between the points (2,3) (-3,1)​

Answer 1

See the picture above hope it will help you. ☺️

Answer 2

Let the points be P (2, 3) and Q (-3, 1)

Use Distance formula :-

$Distance \: PQ \: = \sqrt{( x_{2} - x_{1} ){}^{2} \: + \: ( y_{2} - y_{1} ) {}^{2} }$

Where,

• ${x}_{1}$ = 2
• ${x}_{2}$ = -3
• ${y}_{1}$ = 3
• ${y}_{2}$ = 1

Distance PQ = $= \sqrt{( - 3 - 2) {}^{2} \: + \: (1 - 3) {}^{2} }$

• $\sqrt{( - 5) {}^{2} \: + \: ( - 2) {}^{2} }$

• $\sqrt{( - 5 \times - 5) \: + \: ( - 2 \times - 2)}$

• $\sqrt{25 \: + \: 4}$

• $\sqrt{14.5(2)}$

• $\sqrt{14.5 \times 2}$

• $\sqrt{14.5} \: \times \: \sqrt{2}$

• $7.25 \: \times \: \sqrt{2}$

$= = = > 7.25 \sqrt{2}$

Therefore, the distance between the two pints is 7.25√2