Question:
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
Answer:
x-coordinate of Q is 5
Solution:
Given that,
Point R divides in the ratio 1 : 3
Which means,
Point R divides the line segment PQ internally
The x-coordinate of the point which divides the line segment in ration m:n internally is given as:
[tex]x=(\frac{mx_{2}+nx_{1}}{m+n} )[/tex]
Where,
[tex]x[/tex] = x-coordinate of point dividing the segment R = -1
[tex]x_1[/tex] = x-coordinate of P = -3
[tex]x_2[/tex] = x-coordinate of Q = ?
m : n = 1 : 3
m = 1
n = 3
Therefore,
[tex]-1 = \frac{1 \times x_2 + 3 \times -3}{1+3}\\\\-1 = \frac{x_2 -9}{4}\\\\x_2 - 9 = -4\\\\x_2 = 9 - 4\\\\x_2 = 5[/tex]
Thus x-coordinate of Q is 5
