Question

3. Find the ratio in which the y-axis divides the line seg
/ment joining the
points (-4, -6) and (10, 12).​

Answer 1

Solution :

Let the ratio in which y-axis divides the line segment joining (-4 , -6) and (10 , 12) be k:1 .

Using the formula :

$\boxed{\tt x = \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} }$

Given :

$\tt x_1 = -4 \\ \tt x_2 = 10 \\ \tt m_1 = k \\ \tt m_2 = 1$

Since the line segment is divided by y - axis , the coordinate of the point at which it is divided will have abscissa as 0 . Therefore , the coordinates will be P(0 , y) .

Hence , x = 0

$\implies \tt x = \dfrac{(k \times 10) + (1 \times - 4)}{k + 1} \\ \\ \implies \tt 0 = \frac{10k - 4}{k + 1} \\ \\ \tt \implies 0(k + 1) = 10k - 4 \\ \\ \tt \implies 10k - 4 = 0 \\ \\ \tt \implies 10k = 4 \\ \\ \tt \implies k = \frac{4}{10} \\ \\ \implies \boxed{ \tt k = \frac{2}{5} }$

Therefore the ratio in which y - axis divides the line segment is :

$\implies \tt 2: 5 : 1 \\ \\ \implies \boxed{\tt ratio = 2 : 5}$

Answer 2

Answer:

ratio - 2:5

Step-by-step explanation: