Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

Let A = (-5, 8) and B = (10, -4) Let P and Q be points which trisects AB. Let P (a, b) divide AB in 1 : 2 and Q (c, d) in 2 : 1. By section formula (for P), P = (a, b) = (0, 4). By section formula (for Q), Q = (c, d) = (5, 0). Since, x co-ordinate of P = 0, it means P lies on y-axis and y co-ordinate of Q = 0, it means Q lies on x-axis. Hence, proved that line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

The point P(5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.

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Find the co-ordinates of the points of tri-section of the line joining the points (-3, 0) and (6, 6).

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Show that A(3, -2) is a point of trisection of the line-segment joining the points (2, 1) and (5, -8). Also, find the co-ordinates of the other points of trisection.

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The line segment joining the points M(5, 7) and N(-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

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Mathematics

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

Section Formula

Related Questions

The point P(5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.

Find the co-ordinates of the points of tri-section of the line joining the points (-3, 0) and (6, 6).

Show that A(3, -2) is a point of trisection of the line-segment joining the points (2, 1) and (5, -8). Also, find the co-ordinates of the other points of trisection.

The line segment joining the points M(5, 7) and N(-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.