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Solving problem involving coordinates

Solving problem involving coordinates

Secondary 3

The diagram shows the points \(P\left( 0,2 \right)\) and \(Q\left( 0,12 \right)\).
\(QR\) and \(PR\) are straight lines.

  1. Given that the equation of the line \(QR\) is parallel to the line \(y=-2x+5\), write down the equation of the line \(QR\).
  2. If \(PR\) is a horizontal line parallel to the \(x\)-axis, state the equation of \(PR\).
  3. Given that the \(x\)-coordinate of \(R\) is \(r\). Calculate
    1. the value of \(r\).
    2. the length of \(QR\).

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Answer:(i) \(y = -2x + 12\) (ii) \(y = 2\) (iii)(a) \(r = 5\) (iii)(b) \(11.2\) units

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