Question

1. Find the distance between the following pairs of points
EXERCISE 7.1

(1) (2, 3), (4,1)​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

$\; \; \;$  

❏ Find the distance between the following pairs of points :

        ➠ (2 , 3) and (4 , 1)​

$\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \;$  

$\underline{\boxed{\bold{Important\;Information}}}$  

$\; \; \;$  

❏ Distance is an important quantity in geometry. There are many concepts related to distance or can be explained relating with distance !  

 $\; \; \;$  

Here is formula to find distance between two points :

$\; \; \;$  

$\boxed{\bold{\red{:\leadsto \; Distance = \sqrt{(x-a)^2 + (y-b)^2} }}}$

$\; \; \;$  

Here,

➠  Point M = (x , y)

➠ Point N = (a , b)

➠ Distance = Length of line segment MN

$\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \;$  

$\underline{\boxed{\bold{Given}}}$

$\; \; \;$  

➠ Point M = (2 , 3)

➠ Point N = (4 , 1)

 $\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \;$  

$\underline{\boxed{\bold{Answer}}}$

Let's Start !

$\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \;$  

Let's use the formula given below :

 $\; \; \;$  

$\boxed{\bold{\red{:\leadsto \; Distance = \sqrt{(x-a)^2 + (y-b)^2} }}}$

$\; \; \;$  

$\; \; \;$  

$\bold{\blue{:\implies \; MN = \sqrt{(4-2)^2 + (1-3)^2} }}$

$\bold{\orange{:\implies \; MN = \sqrt{2^2 + (-2)^2} }}$

$\bold{\blue{:\implies \; MN = \sqrt{4 + 4} }}$

$\bold{\orange{:\implies \; MN = \sqrt{8} }}$

$\bold{\blue{:\implies \; MN = \sqrt{2 \times 2 \times 2} }}$

$\boxed{\bold{\pink{:\longmapsto \; MN = 2\sqrt{ 2} \; units }}}$

 $\; \; \;$  

$\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \;$  

$\boxed{\boxed{\bold{\therefore Distance \; between \; 2 \; given \; points = 2\sqrt{ 2} \; units}}}$

 $\; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\; \; \;$  

Hope this helps u.../

【Brainly Advisor】