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Question

If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q 53, b, Then,

(a) a = 83, b = 23

(b) a = 73, b = 0

(c) a = 13, b = 1

(d) a = 23, b = 13

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Solution

We have two points A (3,−4) and B (1, 2). There are two points P (a,−2) and Q which trisect the line segment joining A and B.

Now according to the section formula if any point P divides a line segment joining andin the ratio m: n internally than,

The point P is the point of trisection of the line segment AB. So, P divides AB in the ratio 1: 2

Now we will use section formula to find the co-ordinates of unknown point A as,

Equate the individual terms on both the sides. We get,

Similarly, the point Q is the point of trisection of the line segment AB. So, Q divides AB in the ratio 2: 1

Now we will use section formula to find the co-ordinates of unknown point A as,

Equate the individual terms on both the sides. We get,

So the answer is (b)


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