Question

In what ratio does the point on y-axis divides the line segment joining the Points A(–2, –3) and B(2, –1).

Answer 1

Let the Point which is dividing them be P and its coordinates be (x, y).

Since its y axis it is(0 , y).

And the ratio be $m_1 \: and \: m_2$

BY SECTION FORMULA WE KNOW,

$\boxed{x = \frac{m_1 \times x_2 + m_2 \times x_1}{m_1 + m_2}}$

$\mathsf{0 = \frac{m_1 \times (2) + m_2 \times (-2)}{m_1 + m_2}}$

$\mathsf{0 = 2 m_1+ - 2 m_2 }$

$\mathsf{2 m_2 = 3m_1}$

$\mathsf{ \frac{2}{2} = \frac{m_1}{m_2}}$

$\mathsf{ \frac{1}{1} = \frac{m_1}{m_2}}$

FOR COORDINATE OF y,

we can either use section Formula or mid Point formula because the ratio in which they are divided is same.

By midpoint theorem,

$\boxed{y = \frac{y_1 + y_2}{2}}$

$\mathsf{y = \frac{(-1) + (-3)}{2}}$

$\mathsf{y = \frac{- 4}{2}}$

$\huge \boxed{y = -2}$

So, the coordinates of y axis be (0 , -2)

and the ratio in which they are divided is 1 : 1.