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Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?

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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

Learn more about line division here:

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