Point R divides PO 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:The x-coordinate of Q is 5Step-by-step explanation:* Lets revise the division of the line segment- If point (x , y) divides a line segment internally whose endpoints are  (x1 , y1) and (x2 , y2) at the ratio m1 : m2 from (x1 , y1), then:# [tex]x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}[/tex]# [tex]y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}[/tex]* Lets solve the problem∵ Point R divides PQ in the ratio 1 : 3∴ R is (x , y) ∴ P is (x1 , y1) and Q is (x2 , y2)∴ m1 = 1 and m2 = 3∵ x-coordinate of R is -1 and the x-coordinate of P is -3∴ x = -1 ∴ x1 = -3- Use the rule above∵ [tex]-1=\frac{(3)(-3)+(1)(x_{2})}{1+3}=\frac{-9+x_{2}}{4}[/tex]- By cross multiplication∴ (-1) (4) = -9 + x2∴ -4 = -9 + x2 ⇒ add 9 to both sides∴ 5 = x2* The x-coordinate of Q is 5