Question

Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the x-axis. Also find the coordinates of the points of division​

Answer 1

Answer:

Find the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.

Answer:

We have to find ratio

Let us assume the ratio be k : 1

Hence, m1= k, m2= 1

x1= 1, y1= −5

x2= −4, y2= 5

Also, x = x, y = 0

Using section formula for y-axis

\(y=\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\) \(0=\frac{k\times 5 + 1\times (-5)}{k+ 1}\) \(0=\frac{5k -5}{k+ 1}\)

5k – 5 = 0

5k = 5

k = 1

Which means x-axis will divide the line segment in a ratio 1:1, externally.

Using section formula for x-axis

\(x=\frac{m_{1}x_{2}+m_{2}x_{2}}{m_{1}+m_{2}}\) \(x=\frac{k\times (-4) + 1\times 1}{k+ 1}\) \(x=\frac{1\times (-4) + 1\times 1}{1 + 1}\) \(x=\frac{-4 + 1}{2}\)

x = -3/2

Hence, the coordinate of point is P(x,0) that is (-3/2, 0).

Step-by-step explanation:

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Answer 2

The ans will be whole sum will be 23