Math, asked by rewantdumbhare6490, 1 year ago

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

Answers

Answered by nain31
7

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.

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