Question

2.Find the distance between the following pair of points-

(3,2) and (6,6)

(0, 0) and (6, 1)

(-6, 0) and(4, 0)​

Answer 1

Answer:

1.. 5 units

2.. root 37 units

3.. 10 units.

hope it hlps u mate....

Answer 2

◔ Question :

Find the distance between the following pair of points :

1) (3 , 2) and (6 , 6)

1) (0 , 0) and (6 , 1)

1) (-6 , 0) and (4 , 0)

» To Find :

The distance between the points.

» We Know :

Distance Formula :

$\Longrightarrow \purple{\sf{\underline{\boxed{\sqrt{\left(x_{2} - x_{1}\right)^{2} + \left(y_{2} - y_{1}\right)^{2}}}}}}$

Where $\sf{x_{1}}$ , $\sf{x_{2}}$ , $\sf{y_{1}}$ and $\sf{y_{2}}$ are the points lying in the co-ordinates.

◔ Solution :

For points (3 , 2) and (6 , 6)

» Given :

• $\sf{x_{1} = 3}$

• $\sf{x_{2} = 6}$

• $\sf{y_{1} = 2}$

• $\sf{y_{2} = 6}$

» Calculation :

Using the Formula and Substituting the values in it ,we get :

$\purple{\sf{\sqrt{\left(x_{2} - x_{1}\right)^{2} + \left(y_{2} - y_{1}\right)^{2}}}}$

$\sf{\Rightarrow \sqrt{\left(6 - 3\right)^{2} + \left(6 - 2\right)^{2}}}$

$\sf{\Rightarrow \sqrt{3^{2} + 4^{2}}}$

$\sf{\Rightarrow \sqrt{9 + 16}}$

$\sf{\Rightarrow \sqrt{25}}$

$\purple{\sf{\Rightarrow 5}}$

Hence ,the distance between the points (3 , 2) and (6 , 6) is 5 units.

For points (3 , 2) and (6 , 1)

» Given :

$\sf{x_{1} = 0}$

$\sf{x_{2} = 6}$

$\sf{y_{1} = 0}$

$\sf{y_{2} = 1}$

» Calculation :

Using the Formula and Substituting the values in it ,we get :

$\purple{\sf{\sqrt{\left(x_{2} - x_{1}\right)^{2} + \left(y_{2} - y_{1}\right)^{2}}}}$

$\sf{\Rightarrow \sqrt{\left(6 - 0\right)^{2} + \left(1 - 0\right)^{2}}}$

$\sf{\Rightarrow \sqrt{6^{2} + 1}}$

$\sf{\Rightarrow \sqrt{36 + 1}}$

$\purple{\sf{\Rightarrow \sqrt{37}}}$

Hence ,the distance between the points (0 , 0) and (6 , 1) is √37 units.

For points (-6 , 0) and (4 , 0)

» Given :

$\sf{x_{1} = -6}$

$\sf{x_{2} = 4}$

$\sf{y_{1} = 0}$

$\sf{y_{2} = 0}$

» Calculation :

Using the Formula and Substituting the values in it ,we get :

$\purple{\sf{\sqrt{\left(x_{2} - x_{1}\right)^{2} + \left(y_{2} - y_{1}\right)^{2}}}}$

$\sf{\Rightarrow \sqrt{\left(4 - (-6)\right)^{2} + \left(0 - 0\right)^{2}}}$

$\sf{\Rightarrow \sqrt{\left(4 + 6\right)^{2} + \left(0 - 0\right)^{2}}}$

$\sf{\Rightarrow \sqrt{10^{2} + 0}}$

$\sf{\Rightarrow \sqrt{100}}$

$\purple{\sf{\Rightarrow 10}}$

Hence ,the distance between the points (-6 , 0) and (4 , 0) is 10 units.

» Additional information :

• The distance between the points (x , y) from the origin (0,0)

=> $\sf{\sqrt{x^{2} + y^{2}}}$

• Distance Formula can be also written as

$\sf{\sqrt{\left(x_{1} - x_{2}\right)^{2} + \left(y_{1} - y_{2}\right)^{2}}}$