Question

③ In which ratio does x-anis divide the
line segment joining A (1, 2) and B (-4,-5) from A ​

Answer 1

✬ The required ratio of x axis is 2:5 ✬

Step-by-step explanation:

Given:-

• The X-axis divides the line segment joining A(1,2) and B(-4,-5).

To find:-

• Ratio of the line segments AB

Method 1:

Required Formula:

• X-axis divides AB in the ratio = -y1:y2

ATQ, Let the ratio be A(x1,y1) = (1,2) and B(x2,y2) = (-4,-5)

Then,

$\\ :\implies\sf{-y_1:y_2= \cancel{-} \: 2 : \cancel{- } \: 5} \\ \\ :\implies\underbrace{\boxed{\frak{-y_1:y_2=2 : 5}}}\:\blue{\bigstar}$

• Therefore,The required ratio is 2:5.

Method 2:

Required Formula:

• Point on x-axis is (a,0)
• A,0 = mx2+nx1/m+n, my2+ny1/m+n

Then,

$\\ :\implies\sf{a = \frac{m( - 4) + n(1)}{m + n} ,0= \frac{m( - 5) + n(2)}{m + n} } \\ \\ :\implies\sf{0= \frac{ - 5m + 2n}{ 0} } \\ \\ :\implies\sf{ - 5 m + 2n= 0} \\ \\ :\implies\sf{ - 5m = - 2n} \\ \\ :\implies\sf{ \frac{m}{n} = \frac{ \cancel{ -} \: 2}{ \cancel{ - } \: 5} } \\ \\ :\implies\sf{ \frac{m}{n} = \frac{2}{5} } \\ \\ :\implies \underbrace{ \boxed{\frak{m : n = 2 :5 }}} \: \pink{ \bigstar}$

• Therefore,the required ratio is 2:5

Answer 2

Answer:

Therefore, x-axis divide the line segment joining p (-4 -6) and q (-1,7) is 6:7. Therefore, the coordinates of the point of division are . The point p which divides the line segment joining points a(2,-5) and b(5,2) in the ratio 2:3 lies