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1. Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3

   The question has to do with line division

   What is line division?

   This is the division of a line into a given ratio.

   How to find the coordinate of Q?

   Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.

   Let

   • x₁ = coordinate of P = -3,
   • x₂ = coordinate of R = -3 and
   • x₃= coordinate of Q.

   Since R divides PQ in the ratio, 1:3, we have that

   PR/RQ = 1/3

   (x₂ – x₁)/(x₃ – x₂) = 1/3

   Substituting the values of the variables into the equation, we have

   (x₂ – x₁)/(x₃ – x₂) = 1/3

   (-1 – (-3))/(x₃ – (-3)) = 1/3

   (-1 + 3)/(x₃ + 3) = 1/3

   2/(x₃ + 3) = 1/3

   x₃ + 3 = 2 × 3

   x₃ + 3 = 6

   x₃ = 6 – 3

   x₃ = 3

   So, the x-coordinate of Q is 3

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