Question

In a cinema hall, people are seated at a distance of 1 m from each other, to maintain social distance due to CORONA virus pandemic. Let three people sit at points P, Q and R whose coordinates are (6,-2), (9,4), and (10,6) respectively

the ratio in which q divides the line segment joining p and r is?​

Answer 1

Given: In a cinema hall, people are seated at a distance of 1 m from each other, to maintain social distance due to CORONA virus pandemic. Let three people sit at points P, Q and R whose coordinates are (6,-2), (9,4), and (10,6) respectively.

To find: Ratio in which Q divides the line segment joining P and R

Solution: Coordinates of P ( 6,-2)

Coordinates of Q (9,4)

Coordinates of R (10,6)

Here, Q is the point of division. Let the ratio of division be k:1.

The section formula is used to find the point of division. The formula is:

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

where (x,y) are coordinates of the point of division

Here, (x,y) = Coordinates of Q

(x1,y1)= Coordinates of P

(x2,y2)= Coordinates of R

Therefore,

x = 9 ,y = 4, x1= 6, y1= -2, x2= 10 and y2= 6

The value of m and n are k and 1 respectively.

Using values:

(9,4) = k×10+1×6/k+1, k×6+ 1×-2/k+1

(9,4) = 10k+6/k+1 , 6k-2/k+1

Therefore, equating x-coordinate:

10k+6/k+1 = 9

=> 10k+6 = 9(k+1)

=> 10k+6= 9k+9

=> 10k-9k = 9-6

=> k = 3

Ratio of division

= k:1

=3:1

Therefore, Q divides the line segment joining P and R in the ratio 3:1 respectively.