Math, asked by asree5771, 1 month ago

The point (-3. p) divides the line-seRment joining he points (-5, - 4) and (- 2, 3) internally in the ratio 2: 1. The value of p is


Answers

Answered by MrMonarque
9

Hello, Buddy!!

ɢɪᴠᴇɴ:-

  • A(-5,-4) & B(-2,3) are the end points of a ling segment.
  • (-3,p) divides the line segment in the ratio of 2:1.

ᴛᴏ ꜰɪɴᴅ:-

  • The value of p.

ʀᴇQᴜɪʀᴇᴅ ꜱᴏʟᴜᴛɪᴏɴ:-

Let, m = 2 & n = 1

WKT

  • (x,y) = [mx2+nx1/m+n, my2+ny1/m+n]

Where, (x,y) is the point that divides a line segment in the ratio of m:n

→ (-3,p) = [2(-2)+1(-5)/2+1, 2(3)+1(-4)/2+1]

→ (-3,p) = [(-4-5)/3, (6-4)/3]

→ (-3,p) = [(-9)/3, 2/3]

→ (-3,p) = [-3, 2/3]

  • Value of p ☞ 2/3

@MrMonarque

Hope It Helps You ✌️

Answered by IIMrVelvetII
13

Given :-

  • A(-5, -4) and B(-2, 3) are the end points of a line segment.
  • (-3, p) divides the line segment into ratio of 2:1.

To Find :-

  • The value of p in (-3, p).

Solution :-

Let, m = 2 and n = 1.

We know that,

 \sf (x, y) = [ \frac{mx_2 + nx_1}{m + n}, \: \frac{my_2 + ny_2}{m + n}]

Here, (x, y) is the point that divides a line segment in the ratio of m:n

 \sf →( - 3,p) = [ \frac{2( - 2) + 1( - 5)}{2 + 1}, \:  \frac{2(3) + 1( - 4)}{2 + 1} ]

 \sf →( - 3,p) = [ \frac{( - 4 - 5)}{3}, \:  \frac{(6 - 4)}{3} ]

 \sf →( - 3,p) = [ - 3, \frac{2}{3} ]

Hence the value of  \sf \fbox{p =  \frac{2}{3}}.

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