Question

ꜰɪɴᴅ ᴛʜᴇ ᴅɪꜱᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ꜰᴏʟʟᴏᴡɪɴɢ ᴘᴀɪʀꜱ ᴏꜰ ᴘᴏɪɴᴛꜱ:
(ɪ) (2, 3), (4, 1)
(ɪɪ) (-5, 7), (-1, 3)
(ɪɪɪ) (ᴀ, ʙ), (-ᴀ, -ʙ)

# ռօ ֆքǟʍʍɨռɢ​

Answer 1

Formula for finding Distance between two points:

= $\sqrt{{(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

━━━━━━━━━━━━━━━

Q1.

Points :

• 2,3
• 4,1

Let,

• x1 = 2
• x2 = 4
• y1 = 3
• y2 = 1

Now by Distance formula:

Distance between them:-

$\sqrt{ {(4 - 2)}^{2} + {(1 - 3)}^{2} }$

$= \sqrt{ {2}^{2} + {( - 2)}^{2} }$

$= \sqrt{4 + 4}$

$= \sqrt{8}$

$\red{\boxed{\bold{\large{= 2 \sqrt{2} units}}}}$

━━━━━━━━━━━━━━━

Q2.

Points:-

• -5 , 7
• -1 , 3

Let,

• x1 = -5
• x2 = -1
• y1 = 7
• y2 = 3

Now by Distance formula:

Distance between them:-

$\sqrt{ {(-5 - (-1))}^{2} + {(3- 7)}^{2} }$

$= \sqrt{ {-4}^{2} + {( -4)}^{2} }$

$= \sqrt{16 + 16}$

$= \sqrt{32}$

$\red{\boxed{\bold{\large{ = 4 \sqrt{2} units}}}}$

━━━━━━━━━━━━━━━

Q.3

Points :

• A, B
• -A , -B

Let,

• x1 = A
• x2= -A
• y1 = B
• y2 = -B

Now by Distance formula:

Distance between them:-

$\sqrt{ {(-A - A)}^{2} + {(-B- B)}^{2} }$

$= \sqrt{ {-2A}^{2} + {( - 2B)}^{2} }$

$= \sqrt{4{A}^{2} + 4{B}^{2}}$

$\red{\boxed{\bold{\large{ = 2 \sqrt{{A}^{2}+{B}^{2}units}}}}}$

or,

$= 2 \sqrt{{(A - B)}^{2}+ 2AB} units$

$\red{\boxed{\bold{\large{ = 2 (A- B) \sqrt {2AB}units}}}}$