SATHEE: Straight Line and Pair of Straight Lines 3 Question 12

Straight Line and Pair of Straight Lines 3 Question 12

13. The coordinates of $A, B, C$ are $(6, 3), (- 3, 5), (4, - 2)$ respectively and $P$ is any point $(x, y)$ . Show that the ratio of the areas of the triangles $△ P B C$ and $△ A B C$ is $| \frac{x + y - 2}{7} |$ .

$(1983, 2 M)$

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Solution:

Area of $△ P B C = \frac{\frac{1}{2} | x (5 + 2) + (- 3) (- 2 - y) + 4 (y - 5) |}{\frac{1}{2} | 6 (5 + 2) + (- 3) (- 2 - 3) + 4 (3 - 5) |}$

$= \frac{| 7 x + 7 y - 14 |}{| 42 + 15 - 8 |} = \frac{7 | x + y - 2 |}{49} = \frac{x + y - 2}{7}$

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Straight Line and Pair of Straight Lines 3 Question 12

13. The coordinates of A,B,C are (6,3),(−3,5),(4,−2) respectively and P is any point (x,y). Show that the ratio of the areas of the triangles △PBC and △ABC is |x+y−27|.

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13. The coordinates of $A, B, C$ are $(6, 3), (- 3, 5), (4, - 2)$ respectively and $P$ is any point $(x, y)$ . Show that the ratio of the areas of the triangles $△ P B C$ and $△ A B C$ is $| \frac{x + y - 2}{7} |$ .