Q. 10

# Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(-4, -8).

Answer :

let The points of trisection of a given line AB be P and Q

Then the ratio AP:PQ:QB = 1:1:1

Hence we get AP:PB = 1:2

And AQ:QB = 2:1

A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by

and

To find point P(x,y)

x = 0

y = 2

To find the point Q(x',y')

x' = -2

y' = -3

Hence point P = (0,2) and Q = (-2,-3)

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Solve any the three sub-questions:

Find the equation of the line passing through the points (4,-5) and (-1,-2).

Maharashtra Board - Geometry PapersSolve sub-questions:

Show that ABCD is a parallelogram if A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)

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Find the area of the sector whose arc length and radius are 14 cm and 6 cm respectively.

Maharashtra Board - Geometry PapersFind the ratio in which the line segment joining the points A(3,8) and B(-9, 3)is divided by the Y-axis.

MHB - Mathematics Part-2Given A(4,-3), B(8,5). Find the coordinates of the point that divides segmentAB in the ratio 3 : 1.

MHB - Mathematics Part-2Find the coordinates of the midpoint of the line segment joining P(0,6)and Q(12,20).

MHB - Mathematics Part-2If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

MHB - Mathematics Part-2In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.

(1) P(-3, 7), Q(1, -4), a:b = 2:1

(2) P(-2, -5), Q(4, 3), a:b = 3:4

(3) P(2, 6), Q(-4, 1), a:b = 1:2

MHB - Mathematics Part-2