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 point of division​

Answer 1

Answer:

Explanation:

Given :

• Points are A(1 , -5) & B(-4 , 5).

To Find :

• Ratio of line segment which is divided by x - axis & coordinates of the point of division.

Solution :

According to the question,

The line segment joining A(1, -5) and B(-4, 5) is divided by the x – axis.

.°. y - axis is 0.

We need to find "Ratio of line segment which is divided by x - axis", So ;

Apply section formula,

y = my2 + ny1/m + n

=> 0 = m × 5 + n × -5/m + n

=> 0(m + n) = 5m - 5n

=> 0 = 5m - 5n

=> 5m = 5n

=> m : n = 1 : 1

Now,

We need to "coordinate of the point of division", So ;

Apply section formula,

x = mx2 + nx1/m + n & y = my2 + ny1/ m + n

=> x = 1 × -4 + 1 × 1/1 + 1 & y = 1 × 5 + 1 × -5/1 + 1

=> x = -4 + 1/2 & y = 5 - 5/2

=> x = -3/2 & y = 0/2

=> x = -3/2 & y = 0

.°. (x, y) = (-3/2 , 0)

Hence :

Ratio of line segment which is divided by x - axis and coordinates of the point of division is 1 : 1 and (-3/2 , 0) respectively.

Answer 2

$\Huge\mathbb\colorbox{orange}{{\color{black}{ANSWER࿐}}}$

$\huge\orange{GIVEN :}$

$\orange\bigstar$ Points that are given= A(1, -5) & B(-4, 5).

$\huge\orange{TO \: FIND :}$

$\orange\bigstar$ Find the ratio in which the line segment joining the points is divided by the x - axis & also find the coordinates of the point of division.

$\huge\orange{SOLUTION :}$

The line segment joining the points is divided by the x - axis,

$\orange\bigstar$ Therefore, y - axis is 0.

The Ratio in which the line segment is divided by the x - axis,

Applying Section Formula,

$y = my2 + \frac{ny1}{m} + n$

$→0 = m \times 5 + n \times \frac{ - 5}{m} + n$

$→0(m + n) = 5m - 5n$

$→0 = 5m - 5n$

$→5m = 5n$

$→m:n = 1:1$

The coordinates of the point of division,

Applying Section Formula,

x = m × 2 + n × 1/m + n and y = my2 + ny1/n + n

→ x = 1 × - 4 + 1 × 1/1 + 1 and y = 1 × 5 + 1 × -5/1 + 1

→ x = -4 + 1/2 and y = 5 - 5/2

→ x = -3/2 and y = 0/2

→ x = -3/2 and y = 0

Hence, the Ratio in which the line segment joining the points is divided by the x - axis is 1:1 & the coordinates of point of division are (-3/2, 0).

Hope it Helps Buddy ❤️

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