Q39 of 149 Page 14

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

Given points are A(-2, -2) and B(2, -4). Let P be (x, y)


Here given that AP = AB.


But AB = AP + BP


∴7AP = 3AB


7AP = 3(AP + BP)


∴4AP = 3BP


∴ =



By section formula,


x = , y =


For point P on AB, where m = 3 and n = 4


x = , y =


x = and y =


Hence, required coordinates is P( , )


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37

The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q . If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.

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

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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?