Challenging +1.2 This is a multi-step coordinate geometry problem requiring students to set up a coordinate system, use perpendicularity and midpoint conditions, apply trigonometry to find coordinates, and solve resulting equations. While it involves several techniques (coordinate setup, perpendicular lines, equal angles, distance formula), the approach is relatively standard for AS-level and the geometric constraints guide the solution method clearly. It's moderately harder than average due to the algebraic manipulation required, but doesn't require exceptional insight.
4 The perpendicular lines AC and BD intersect at E as shown in the diagram. The point E is the midpoint of AC . The angles BAC and BDC are each equal to \(\chi ^ { \circ }\). The lengths of AB and CD are 4 cm and 7 cm respectively.
\includegraphics[max width=\textwidth, alt={}, center]{b5c47a93-ce43-4aa1-ba7f-fbb650523373-3_606_529_1370_244}
Determine the value of \(x\).
Uses basic trig ratio. Also allow use of Pythagoras and another trig ratio instead
So \(x = 29.7\)
A1
cao
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $AE = 4\cos x°$, $EC = 7\sin x°$ | M1* | Uses basic trig to find an expression for either AE or EC |
| E is midpoint so $4\cos x° = 7\sin x°$ | M1 | Equates their expressions |
| So $\frac{\sin x°}{\cos x°} = \tan x° = \frac{4}{7}$ | M1(dep) | Uses a correct trig identity leading to a value for $\tan x$ or equivalent |
| So $x = 29.7$ | A1 [4] | cao |
| **Alternative:** Triangles BAE and CDE are similar with scale factor 1.75, Let $AE = y$ cm $= CE$, $DE = 1.75y$ | M1*, M1 | Identifying similar triangles and scale factor; uses scale factor to find expression for DE or BE as $\frac{4}{7}y$ |
| $\tan x° = \frac{CE}{DE} = \frac{y}{1.75y} = \frac{4}{7}$ | M1(dep) | Uses basic trig ratio. Also allow use of Pythagoras and another trig ratio instead |
| So $x = 29.7$ | A1 | cao |
---
4 The perpendicular lines AC and BD intersect at E as shown in the diagram. The point E is the midpoint of AC . The angles BAC and BDC are each equal to $\chi ^ { \circ }$. The lengths of AB and CD are 4 cm and 7 cm respectively.\\
\includegraphics[max width=\textwidth, alt={}, center]{b5c47a93-ce43-4aa1-ba7f-fbb650523373-3_606_529_1370_244}
Determine the value of $x$.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2024 Q4 [4]}}