Question

Find the point which divides the line segment joining A(-2,-1) and B(7,8) from A in the ratio 1 : 2​

Answer 1

SOLUTION :-

We have to find the coordinates of the point which divides the line segment joining A ( -2 , -1 ) and B ( 7 , 8 ) from A in the ratio 1 : 2.

We can use section formula to find the coordinates of the point.

According to the section formula,

$\bullet\bf \ x \ coordinate = \dfrac{mx_2+nx_1}{m+n} \\\\\\\bullet \ y \ coordinate = \dfrac{my_2+ny_1}{m+n}$

Here,

$\bullet\sf \ x_1= -2 \\\\\bullet \ x_2= 7 \\\\\bullet \ y_1= -1 \\\\\bullet \ y_2= 8 \\\\\bullet \ m = 1\\\\\bullet \ n = 2$

$\longrightarrow\sf x \ coordinate = \dfrac{(1\times 7)+( 2\times -2)}{1+2}$

                         $= \sf \dfrac{7-4}{3} \\\\= \dfrac{3}{3}\\\\= \bf 1$

$\longrightarrow\sf y \ coordinate = \dfrac{(1\times 8 ) +( 2\times -1 )}{1+2}$

                          $= \sf \dfrac{8-2}{3}\\ \\= \dfrac{6}{3}\\\\= \bf 2$

Coordinates of the point = ( 1 , 2 )

Answer 2

$\huge\underline{\pink{{Question:-}}}$

Fɪɴᴅ ᴛʜᴇ ᴘᴏɪɴᴛ ᴡʜɪᴄʜ ᴅɪᴠɪᴅᴇs ᴛʜᴇ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ᴊᴏɪɴɪɴɢ A(-2,-1) ᴀɴᴅ B(7,8) ғʀᴏᴍ A ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1 : 2.

$\huge\underline{\purple{{To find:-}}}$

Tʜᴇ ᴄᴏᴏʀᴅɪɴᴀᴛᴇ ᴏғ ᴘᴏɪɴᴛs ᴡʜɪᴄʜ ᴅɪᴠɪᴅᴇ ᴛʜᴇ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ɪɴᴛᴇʀɴᴀʟʏ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1 : 2.

$\huge\underline{\pink{{Let's take:-}}}$

C Dɪᴠɪᴅᴇs ᴛʜᴇ sᴇɢᴍᴇɴᴛ AB ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1 : 2 ʜᴇɴᴄᴇ ᴍ = 1, ɴ= 2.

Bʏ sᴇᴄᴛɪᴏɴ ғᴏʟᴍᴜʟᴀ ᴡʜɪᴄʜ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴡʜᴇɴ ᴛʜᴇ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ɪs ᴅɪᴠɪᴅᴇᴅ ɪɴᴛᴇʀɴᴀʟʟʏ ʙʏ ᴛʜᴇ ᴘᴏɪɴᴛ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ ᴍ : ɴ ᴛʜᴇɴ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴛʜᴇ ᴘᴏɪɴᴛs ᴀʀᴇ

= C = ᴍx²+ɴx¹/ ᴍ + ɴ , ᴍʏ²+ɴ¹/ ᴍ + ɴ

= (1)(4) + (2)(1)/1+2

= 6/3 , 3/3

= (2,1)

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