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Sequences And Series

Question
CBSEENMA11015494
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The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is

  • 2 plus square root of 2
  • 2 minus square root of 2
  • 1 plus square root of 2
  • 1 minus square root of 2

Solution

B.

2 minus square root of 2

Given mid points of sides of a triangle are (0,1) (1,1) and (1,0). Plotting these points on a graph and make a triangle.

straight x minus coordinate space space equals space fraction numerator ax subscript 1 space plus bx subscript 2 plus cx subscript 3 over denominator straight a plus straight b plus straight c end fraction space equals space fraction numerator 2 space straight x space 2 space plus 2 square root of 2 space straight x 0 space plus 2 straight x 0 over denominator 2 plus 2 plus 2 square root of 2 end fraction space equals space fraction numerator 4 over denominator 4 plus 2 square root of 2 end fraction space equals space fraction numerator 2 over denominator 2 plus square root of 2 end fraction space equals space 2 minus square root of 2

Some More Questions From Sequences and Series Chapter

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

A point lies on the x-axis at a distance of 5 units towards OX'. What are its co-ordinates?

A point lies on z-axis at a distance of 3 units in the direction OZ. Write its co-ordinates.

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