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?
A.

B.
3
C.
5
D.
6
E.
-9



PLEASE HELP

Answer 1

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:

$x=(\frac{mx_{2}+nx_{1}}{m+n} )$

Where,

$x$ = x-coordinate of point dividing the segment R = -1

$x_1$ = x-coordinate of P = -3

$x_2$ = x-coordinate of Q = ?

m : n = 1 : 3

m = 1

n = 3

Therefore,

$-1 = \frac{1 \times x_2 + 3 \times -3}{1+3}\\\\-1 = \frac{x_2 -9}{4}\\\\x_2 - 9 = -4\\\\x_2 = 9 - 4\\\\x_2 = 5$

Thus x-coordinate of Q is 5