Question

A point R with x-coordinate 4 lies on the line joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the co-ordinates of point R.

Solution

Let point R (4, y, z) divide the join of P (2, - 3, 4) and Q (8, 0, 10) in the ratio k:1.
$rightwards double arrow$ R is $open parentheses fraction numerator 8 straight k plus 2 over denominator straight k plus 1 end fraction comma space fraction numerator 0 straight k minus 3 over denominator straight k plus 1 end fraction comma space fraction numerator 10 straight k plus 4 over denominator straight k plus 1 end fraction close parentheses$
∴ $open parentheses fraction numerator 8 straight k plus 2 over denominator straight k plus 1 end fraction comma space fraction numerator negative 3 over denominator straight k plus 1 end fraction comma space fraction numerator 10 straight k plus 4 over denominator straight k plus 1 end fraction close parentheses space left right arrow space left parenthesis 4 comma space straight y comma space straight z right parenthesis$

$rightwards double arrow$ $fraction numerator 8 straight k plus 2 over denominator straight k plus 1 end fraction equals 4 space rightwards double arrow space 8 straight k plus 2 space equals space 4 straight k plus 4 space rightwards double arrow space 4 straight k space equals space 2 space rightwards double arrow space straight k equals 1 half$
∴ $straight y equals fraction numerator negative 3 over denominator begin display style 1 half end style plus 1 end fraction equals space minus 3 cross times 2 over 3 equals negative 2 comma space straight z space equals space fraction numerator 10 straight k plus 4 over denominator straight k plus 1 end fraction equals fraction numerator 10 open parentheses begin display style 1 half end style close parentheses plus 4 over denominator begin display style 1 half end style plus 1 end fraction equals fraction numerator 9 over denominator begin display style 3 over 2 end style end fraction equals 6$
Hence, point R is (4, -2, 6).

Some More Questions From Sequences and Series Chapter

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.

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Sequences And Series

A point R with x-coordinate 4 lies on the line joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the co-ordinates of point R.

Some More Questions From Sequences and Series Chapter

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.

A point lies on y-axis and is at a distance of 4 units in the direction OY'. Write its co-ordinates.

A point lies on XY-plane with distances 4 units along OX and 3 units along OY. Write its co-ordinates.

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For Daily Free Study Material Join wiredfaculty

Sequences And Series

A point R with x-coordinate 4 lies on the line joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the co-ordinates of point R.

Some More Questions From Sequences and Series Chapter

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.

A point lies on y-axis and is at a distance of 4 units in the direction OY'. Write its co-ordinates.

A point lies on XY-plane with distances 4 units along OX and 3 units along OY. Write its co-ordinates.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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).

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).