Find the ratios in which x axis and y-axis divides the line segment joining the points 2 4 4 3

Question 5 Coordinated Geometry - Exercise 7.3

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Answer:

Let the ratio in which x-axis divides the line segment joining (–4, –6) and (–1, 7) = 1: k.

Then,

x-coordinate becomes (-1 – 4k) / (k + 1)

y-coordinate becomes (7 – 6k) / (k + 1)

Since P lies on x-axis, y coordinate = 0

(7 – 6k) / (k + 1) = 0

7 – 6k = 0

k = 7/6

Therefore, the point of division divides the line segment in the ratio 6 : 7.

Now, m1 = 6 and m2 = 7

By using section formula,

x = (m1x2 + m2x1)/(m1 + m2)

= (6(-1) + 7(-4))/(6+7)

= (-6-28)/13

= -34/13

So, now

y = (6(7) + 7(-6))/(6+7)

= (42-42)/13

= 0

Hence, the coordinates of P are (-34/13, 0)

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In what ratio, does the X axis divides the line segment joining the points 2, 3 and 5, 6? [4 MARKS]

Solution

Formula: 1 Mark Steps: 2 Marks Answer: 1 Mark

Let x-axis cuts the line segment joining the points A (2, -3) and B(5, 6) at (a, 0) and the x-axis divides the line segment AB in the ratio $k:1$.

Using section formula, we have

$0=\frac{k\times 6+1\times (-3)}{k+1}\Rightarrow 6k=3\Rightarrow k=\frac{1}{2}$

$\therefore$ $x-axis$ divides it in the ratio 1 : 2