Higher January 2021 Paper 2 Q18
18 A rectangle \(ABCD\) is to be drawn on a centimetre grid such that
\(A\) has coordinates \((-4, -2)\)
\(B\) has coordinates \((1, 10)\)
\(C\) has coordinates \((19, a)\)
\(D\) has coordinates \((b, c)\)
(a) Work out the value of \(a\), the value of \(b\) and the value of \(c\). (4)
(b) Calculate the perimeter, in centimetres, of rectangle \(ABCD\). (3)
| Scheme | Marks |
|---|---|
| B1 | |
| (Gradient \(AB\) =) \(\dfrac{12}{5}\) oe or eg \(\dfrac{10 - -2}{1 - -4}\) oe | M1 |
| (Gradient \(BC\) =) \(-\dfrac{5}{12}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(a = 2.5\), \(c = -9.5\) | A1 |
| (4) |
Notes
B1: \(b = 14\)
M1: For the gradient of \(AB\)
M1: Ft correct use of \(m_1 \times m_2 = -1\) for their gradient of \(AB\) or \(a = 2.5\) or \(c = -9.5\)
A1: for \(a = 2.5\) and \(c = -9.5\)
| Scheme | Marks |
|---|---|
\((AB =)\;\sqrt{(1 - -4)^2 + (10 - -2)^2}\) \(\left(= \sqrt{5^2 + 12^2}\;(= 13)\right)\) | M1 |
\((BC =)\sqrt{(19 - 1)^2 + (10 - 2.5)^2}\) \(\left(= \sqrt{18^2 + 7.5^2}\;(= 19.5)\right)\) or \(\sqrt{(19 - 1)^2 + (10 - \text{their } a)^2}\) or 1.5 × “13” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 65 | A1 |
| (3) | |
| (7 marks) |
Notes
M1: ft their value of \(a\)