# Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x - Mathematics

Sum

Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x

#### Solution

Let P (x,3) divides the line segment joining the points

A(-4,2) and B(3,6) in the ratio K:1.

Thus , we have

(3k-4)/(k+1)=x;    (6k+2)/(k+1)=3

for

6k+2=3(k+1)

⇒ 6k+2=3k+3

⇒3k=3-2

⇒3k=1⇒k=1/3

∴ Required ratio 1:3

a now  consider the quation (3k-4)/(k+1)=x

Substituting the value of k in the above equation, We have

 (3xx1/3-4)/(1/3+1)= x⇒ -3/(4/3)=x ⇒-9/4=x

∴ x=-9/4

b.AP=sqrt (((-9)/4+4)^2+(3-2)^2)=sqrt(49/16+1)=sqrt(49+16)/16=sqrt(65/16)

⇒ AP=sqrt 65/4 "unit"

Concept: Co-ordinates Expressed as (x,y)
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (C) | Q 15 | Page 183