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Class 10 › Mathematics › Coordinate Geometry
CBSE2026Class Class 10 · Mathematics4 Marks · Long✅ Verified
In the school garden, Arun (A), Babu (B), Chandra (C) and Daya (D) planted flower plants of Sunflower, Rose, Champa and Jasmine respectively at points A(2, 8), B(7, 8), C(9, 3) and D(2, 3) respectively.
(i) Find the distances AB and AD.
(ii) Find BC - CD.
(iii)(a) If Varun wants to plant his flower plant at a point M such that DM : MC = 3 : 2, find the coordinates of M.
OR
(iii)(b) If N divides the line segment AC in the ratio 2 : 3, find the coordinates of N.
(ii) $$BC=\sqrt{(9-7)^2+(3-8)^2}=\sqrt{4+25}=\sqrt{29}$$ $$CD=\sqrt{(2-9)^2+(3-3)^2}=\sqrt{49}=7$$ $$BC-CD=\sqrt{29}-7\approx-1.615$$
(iii)(a) Using section formula, M divides DC in ratio 3:2, D(2,3), C(9,3):
$$M=\left(\frac{3(9)+2(2)}{5},\frac{3(3)+2(3)}{5}\right)=\left(\frac{31}{5},3\right)=(6.2,\ 3)$$
OR
(iii)(b) N divides AC in ratio 2:3, A(2,8), C(9,3):
$$N=\left(\frac{2(9)+3(2)}{5},\frac{2(3)+3(8)}{5}\right)=\left(\frac{24}{5},\frac{30}{5}\right)=(4.8,\ 6)$$
