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Answer
Hint: The section formula for the point (x, y) which divides the line segment joining the points \[({x_1},{y_1})\] and \[({x_2},{y_2})\] in the ratio m:n is given as \[(x,y) = \left( {\dfrac{{m{x_2} + n{x_1}}}{{m + n}},\dfrac{{m{y_2} + n{y_1}}}{{m + n}}} \right)\]. Use this formula to find the ratio in which the x-axis divides the line segment joining the points (1, 2) and (2, 3).Complete step-by-step answer:We need to find the ratio in which the x-axis divides the line segment joining the points (1, 2) and (2, 3).Any point on the x-axis has its y coordinate equal to zero. Hence, let us assume a point (x, 0) that divides the line segment joining the points (1, 2) and (2, 3).The section formula for the point (x, y) which divides the line segment joining the points \[({x_1},{y_1})\] and \[({x_2},{y_2})\] in the ratio m:n is given as follows:\[(x,y) = \left( {\dfrac{{m{x_2} + n{x_1}}}{{m + n}},\dfrac{{m{y_2} + n{y_1}}}{{m + n}}} \right)\]
The ratio in which the y-axis divides two points (x1 , y1) and (x2 , y2) is \[\lambda: 1\]
The co-ordinates of the point dividing two points (x1 , y1) and (x2 , y2) in the ratio m : n is given as,
`(x , y) = ((lambdax_2 + x_1)/(lambda + 1 )) ,((lambday_2 + y_1)/(lamda + 1))` where, `lambda = m/n`
Here the two given points are A(5,−6) and B(−1,−4).
\[(x, y) = \left( \frac{- \lambda + 5}{\lambda + 1}, \frac{- 4\lambda - 6}{\lambda + 1} \right)\]
Since, the y-axis divided the given line, so the x coordinate will be 0.
\[\frac{- \lambda + 5}{\lambda + 1} = 0\]
\[\lambda = \frac{5}{1}\]
Thus the given points are divided by the y-axis in the ratio 5:1.
The co-ordinates of this point (x, y) can be found by using the earlier mentioned formula.
`(x , y ) = ((5/1 (-1) + (5) )/(5/1 + 1)) , ((5/1(-4)+(-6))/(5/1 +1))`
`(x , y) = (0/6) , (-26/6)`
`(x , y ) = ( 0 , - 26/6)`
Thus the co-ordinates of the point which divides the given points in the required ratio are `(0,-26/6)`.
In what ratio does the x axis divide the line segment joining the points 4, 6 and 1,7? Find the coordinates of the point of division.
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In what ratio, does the X axis divides the line segment joining the points 2, 3 and 5, 6? [4 MARKS]
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In what ratio does the x-axis divide the line segment joining the points (-4, -6) and (-1, 7). Also, find the coordinates of the point of division.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Let the line segment joining the points (-4, -6) and (-1, 7) be divided by the point on x-axis (x, 0) in the ratio k: 1.
Using section formula, we have:
Thus, the coordinates of the point of division are
Answered by | 04 Jun, 2014, 03:23: PM