2026 TPSS P2 Q2

2026 TPSS P2 Q2

Secondary 4
8 marks

Triangle \(ABC\) has coordinates \(A\ (-3,4)\), \(B\ (-1,-5)\) and \(C\ (9,-5)\).

  1. Find the equation of \(AC\).[3]
  2. Calculate the length of \(AC\).[1]
  3. Calculate the area of triangle \(ABC\).[1]
  4. State the coordinates of \(D\) such that \(ACDB\) form a parallelogram.[1]
  5. The equation of a line \(p\) is \(4y+3x=4\). Determine if the line \(p\) will intersect line \(AC\). Explain your answer with mathematical working.[2]

Solution:

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Answer:(a) \(y=-\dfrac34x+\dfrac74\) (b) \(15\) units (c) \(45\text{ units}^2\) (d) \((11,-14)\) (e) No; equal gradients and different intercepts.

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