# In What Ratio Does the Point (24/11, Y) Divide the Line Segment Joining the Points P(2, –2) and Q(3, 7)? Also Find the Value of Y. - Mathematics

In what ratio does the point (24/11, y) divide the line segment joining the points P(2, –2) and Q(3, 7)? Also find the value of y.

#### Solution

Let the point P(24/11, y) divide the line PQ in the ratio k : 1.

Then, by the section formula:

x = (mx_2+nx_1)/(m+n), y = (my_2 + ny_1)/(m + n)

The coordinates of R are (24/11, y)

24/11 = (3k + 2)/(k + 1), y = (7k - 2)/(k + 1)

=>24(k + 1) = 33k + 22, y(k + 1)= 7k - 2

2424 = 3322  ,   yy =7− 2

⇒2 = 9k

=> k = 2/9

Now consider the equation yk + y = 7k - 2 and put k = 2/9

=> 2/9y + y = 14/9 - 2

=> 11/9y = (-4)/9

=> y = (-4)/11

Therefore, the point R divides the line PQ in the ratio 2 : 9

And, the coordinates of R are (24/11, (-4)/11)

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