## Question

Find the ratio in which the point (2, *y*) divides the line segment joining (4, 3) and (6, 3) and hence find the value of *y*.

### Solution

3

Let *P* divides *AB* internally in the ratio λ : 1

∴ *P* divides *AB* externally in the ratio 1 : 2 (âˆµ λ is negative)

Now,

#### SIMILAR QUESTIONS

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

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Find the length of median through *A* of a triangle whose vertices are *A*(–1, 3), B(1, – 1)and *C*(5, 1).

Determine the ratio in which *y* – *x* + 2 = 0 divides the line joining (3, –1) and (8, 9).

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Find the coordinates of a point which divides externally the line joining (1, –3) and (–3, 9) in the ratio 1: 3.

The line segment joining *A*(6, 3) to *B*(–1, –4) is doubled in length by having its length added to each end. Find the coordinates of the new ends.

Find the harmonic conjugates of the point *R*(5, 1) with respect to the points *P*(2, 10) and *Q*(6, –2).