2026 MSHS P2 Q2

Secondary 4

10 marks

\(A\) is the point \((-2,4)\) and \(B\) is the point \((4,1)\).
1. Find the length of the line \(AB\).[1]
2. Find the equation of the line \(AB\).[2]
3. The line \(AB\) cuts the \(x\)-axis at \(P\) and the \(y\)-axis at \(Q\).
  Find the area of triangle \(OPQ\) where \(O\) is the origin.[2]
A company manufactures three sizes of glass which are geometrically similar.
The height of the small, medium and large glasses are \(h\) cm, \(8\) cm and \(10\) cm respectively.
1. The top of the large glass has a circumference of \(30\) cm.
  Find the circumference of the top of the medium glass.[1]
2. The surface area of the small glass is \(\dfrac9{16}\) of the surface area of the medium glass.
  Show that \(h=6\).[2]
3. Calculate the ratio of the volume of the small glass to the volume of the large glass.[2]

Similar questions are unavailable for this question.

Answer:(a)(i) \(6.71\) units (ii) \(y=-\dfrac12x+3\) (iii) \(9\text{ units}^2\) (b)(i) \(24\) cm (ii) \(h=6\) (iii) \(27:125\).

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