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Prove that the points (5,1),\ (1,-1)a n ...

Prove that the points `(5,1),\ (1,-1)a n d\ (11 ,4)` are collinear. Also find the equation of the straight line on which these points lie.

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To prove that the points \( (5, 1), (1, -1), \) and \( (11, 4) \) are collinear, we will follow these steps: ### Step 1: Find the equation of the line through two points We will use the points \( (5, 1) \) and \( (1, -1) \) to find the equation of the line. The formula for the equation of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ ...
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RD SHARMA-THE STRAIGHT LINES -Solved Examples And Exercises
  1. Find the equation of the line joining the points (-1,3)a n d\ (4,-2)do...

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  2. Find the equation of the medians of the triangle ABC whose vertices ar...

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  3. Prove that the points (5,1),\ (1,-1)a n d\ (11 ,4) are collinear. Also...

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  4. The Fahrenheit temperature F and absolute temperature K satisfy a li...

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  5. Find the equation of the straight lines passing through the following ...

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  6. Find the equation of the straight lines passing through the following ...

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  7. Find the equation of the straight lines passing through the following ...

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  8. Find the equation of the straight lines passing through the following ...

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  9. Find the equation of the straight lines passing through the following ...

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  10. Find the equation of the straight lines passing through the following ...

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  11. Find the equations to the sides of the triangles of the coordinates of...

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  12. If the coordinates of the vertices of triangle A B C are (-1,6),(-3,-9...

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  13. Find the equation of the side BC of the triangle ABC whose vertices ar...

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  14. By using the concept of equation of a line, prove that the three po...

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  15. Prove that the line y-x+2 =0 divides the join of points (3,-1) and (8,...

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  16. Find the equation to the straight line which bisects the distance b...

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  17. In what ratio is the line joining the points (2,3)a n d\ (4,-5) divide...

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  18. The vertices of a quadrilateral are A(-2,6),\ B(1,2),\ C(10 ,4)a n d D...

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  19. The length L (in centimetre) of a copper rod is a linear function o...

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  20. Find the equation of the line which cuts off an intercept 4 on the ...

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