Q40 of 149 Page 14

Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.

Let given coordinates be A(-2, 2) and B (2, 8).


We need to divide AB into 4 equal parts, ie first we need to find midpoint of AB, which will be D and then find out midpoints of AD and DB respectively.


Let required points be C(x1 , y1 ), D(xm , ym ) and E(x , y2 )



By midpoint formula.


x = , y =


For midpoint D of AB,


xm = , ym =


∴ xm = 0 and ym = 5


∴ D(xm , ym ) ≡ (0 , 5)


Now, for midpoint C of AD,


X1 = , y2 =


x1 = -1 and y1 =


∴C(x1 , y1) ≡ (-1, )


For midpoint E of DB,


X2 = , y2 =


∴ x2 = 1 and y2 =


∴ E(x2 , y2 ) ≡ (1 , )


Hence the co-ordinates of the points are (-1, ) , (0 , 5) and (1 , )


More from this chapter

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38

The line joining the points (2,1) and (5,-8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0. Find the value of k.

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If A and B are two points having coordinates (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB.

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A (4, 2), B (6, 5) and C (1, 4) are the vertices of ABC.

(i) The median from A meets BC in D. Find the coordinates of the point D.


(ii) Find the coordinates of point P on AD such that AP : PD = 2 :1.


(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.


(iv) What do you observe?

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ABCD is a rectangle formed by joining the points A (-1, -1), B (-1, 4), C (5, 4) and D (5,-1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.