Let , and be the vertices of . Point divides internally in the ratio ( ). What is…

MATHEMATICS · Single correct · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Let A(2,1)A(2,1), B(8,5)B(8,5) and C(14,1)C(14,1) be the vertices of △ABC\triangle ABC. Point DD divides BCBC internally in the ratio 1:31:3 (BD:DC=1:3BD:DC=1:3). What is ar⁡(△ABD):ar⁡(△ADC)\operatorname{ar}(\triangle ABD):\operatorname{ar}(\triangle ADC)? (a) 3:13:1 (b) 1:31:3 (c) 1:91:9 (d) 1:41:4

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