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प्रश्न
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
उत्तर
The coordinates 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,
`(x,y) = ((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`
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(3,−2) and B(−3,−4).
So we need to find the points which divide the line joining these two points in the ratio 1: 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(3) + 2(-3))/(1 + 2)), ((1(-2) + 2(-4))/(1 + 2))`
`(e, d) = (-1, -10/3)`
Therefore the points of trisection of the line joining the given points are `(1, 8/3) and (-1, -10/3)`
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संबंधित प्रश्न
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Also, find its area.
Find the points of trisection of the line segment joining the points:
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Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
In which quadrant does the point (-4, -3) lie?
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
(–1, 7) is a point in the II quadrant.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
