Question

The point which divides the line segment joining the points (8,-9) and (2, 3) in ratio 1:2 internally!
lies in the
(a) I quadrant
(b) Il quadrant
(c) III quadrant
(d) IV quadrant
​

Answer 1

hope it helps...it would lie in 4 quadrant

Answer 2

Given:

A line segment joins the points (8,-9) and (2,3).

To find:

The point which divides the given segment in ratio 1:2 internally

Solution:

Let us name the two points given as X(8,-9) and Y(2,3).

Let the point which divides the line segment joining X and Y in ratio 1:2 internally be Z(a, b).

Now, we know by using the section formula we can find out the coordinates of point Z.

(The section formula is used to determine the coordinates of a point that splits a line segment externally or internally in a certain ratio.)

Therefore, by section formula,

Coordinates of Z = (m₁ x₂ + m₂ x₁ / m₁ + m₂, m₁ y₂ + m₂ y₁ / m₁ + m₂)

Here, m₁ and m₂ define the division of the line segment into a ratio m₁:m₂.

= {(1×2 + 2×8) / 1+2 , (1×3 + 2×-9)/ 1+2}

= (6, -5)

Now, here we can see that the x-coordinate of Z is positive and the y-coordinate is negative. Therefore Point Z lies in the fourth quadrant.

Hence, The correct option is (d), IV Quadrant. The point which divides the line segment is in the fourth quadrant.

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