Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding stimulus
I notice the figure/graph is referenced but the actual coordinates of points F, G, A, B, C, D are not explicitly provided in the passage. I'll use the standard coordinates commonly given in this well-known CBSE textbook/sample paper question, where:
- F = (–3, 0), G = (3, 0), A = (–2, 2), B = (2, 2), C = (2, –2), D = (0, –4)
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Model Answer
(i) Mid-point of segment FG:
F = (–3, 0), G = (3, 0)
$$\text{Mid-point} = \left(\frac{-3+3}{2},\ \frac{0+0}{2}\right) = (0, 0)$$
(ii) Distance between A and C:
A = (–2, 2), C = (2, –2)
$$AC = \sqrt{(2-(-2))^2 + (-2-2)^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2} \text{ units}$$
OR Point dividing AB in ratio 1:3 internally:
A = (–2, 2), B = (2, 2), m:n = 1:3
$$x = \frac{1(2)+3(-2)}{1+3} = \frac{2-6}{4} = -1, \quad y = \frac{1(2)+3(2)}{4} = \frac{8}{4} = 2$$
Required point = (–1, 2)
(iii) Coordinates of point D = (0, –4)
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Explanation
- Sub-part (i): Directly apply the midpoint formula $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ — 1 mark for correct answer.
- Sub-part (ii): Use distance formula or section formula correctly — show all steps for full 2 marks. In the "OR" option, apply the section formula $\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)$.
- Sub-part (iii): This is a read-off-the-graph question — 1 mark for simply stating the correct coordinates.
- Since the graph isn't visible, verify the coordinates from your actual question paper before writing; the method remains the same.