Higher November 2024 Paper 3 Q16
16 \(OBCD\) is a rectangle.
\(DCE\) is a straight line.
\(B\) has coordinates \((2, -4)\)
\(E\) has coordinates \((12, -6.5)\)
Work out the coordinates of \(D\).
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| (7, 3.5) | P1 | process to find the gradient of \(OB\), eg \(\dfrac{-4 - 0}{2 - 0}\ (= -2)\) |
| P1 | process to find the equation of \(DE\), eg substitutes \((12, -6.5)\) into \(y = \text{``}{-}2\text{''}x + c\) or \(y = [-2]x + c\) or \(y - -6.5 = \text{``}{-}2\text{''}(x - 12)\) or \(y - -6.5 = [-2](x - 12)\) | |
| P1 | process to find the equation of \(OD\), eg substitutes \((0, 0)\) into \(y = \dfrac{-1}{\text{``}{-}2\text{''}}x + c\) or \(y = \dfrac{-1}{[-2]}x + c\) or \(y - 0 = \dfrac{-1}{\text{``}{-}2\text{''}}(x - 0)\) or \(y - 0 = \dfrac{-1}{[-2]}(x - 0)\) | |
| P1 | (dep P3) forms an equation that can be solved to find \(x\) coordinate of \(D\), eg \(\text{``}{-}2x + 17.5\text{''} = \text{``}\dfrac{1}{2}x\text{''}\) | |
| A1 | cao |
Additional guidance
Equation of \(DE\) is \(y = -2x + 17.5\)
Where [−2] can be \(\dfrac{-1}{2}\) or 2 or \(\dfrac{1}{2}\) and must be labelled as the gradient of \(OB\)
Equation of \(OD\) is \(y = \dfrac{1}{2}x\)
Where [−2] can be \(\dfrac{-1}{2}\) or 2 or \(\dfrac{1}{2}\) and must be labelled as the gradient of \(OB\)
A correct answer with no supportive working gets 0 marks