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प्रश्न
Find the points of trisection of the line segment joining the points:
(2, -2) and (-7, 4).
उत्तर
The co-ordinates of a point which divided two points `(x_1, y_1)` and `(x_2, y_2)` internally in the ratio m:n is given by the formula,
The points of trisection of a line are the points which divide the line into the ratio 1: 2
Here we are asked to find the points of trisection of the line segment joining the points A(2,-2) and B(-7,4).
So we need to find the points which divide the line joining these two points in the ratio1:2 and 2 : 1.
Let P(x, y) be the point which divides the line joining ‘AB’ in the ratio 1 : 2.
`(x,y) = (((1(-7) + 2(2))/(1 + 2))"," ((1(4) + 2(-2))/(1+2)))`
(x,y) = (-1,0)
Let Q(e, d) be the point which divides the line joining ‘AB’ in the ratio 2 : 1.
`(e, d) = (((1(2) + 2(7))/(1 + 2))"," ((1(-2) + 2(4))/(1 + 2)))`
(e, d)= (-4, 2)
Therefore the points of trisection of the line joining the given points are (-1, 0) and (-4, 2)
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Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
