Question

if point t divides the segments AB with A(-7,4) and B (-6,-5) in the ratio 7:2,find the coordinates of t.
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Answer 1

Answer:

Coordinates of t $\bf \bigg( \dfrac{ - 56}{9} \bigg) \: - 3$

Explanation:

Given that,

The point ‘t’ divides a line segment AB with A(-7, 4) and B(-6, -5) in the ratio 7 : 2

By section formula :-

If t divides the line segment AB in the ratio $\bf m_1 : m_2$

${ \longrightarrow \sf t = \bigg(\dfrac{m_1x_1 + m_2x_2}{m_1 + m_2}\bigg)\bigg(\dfrac{m_1y_1 + m_2y_2}{m_1 + m_2}\bigg) \: }$

Where,

$\sf \bull \: m_1 =7 \: and \: m_2 = 2$

$\bull \sf \: x_1= - 7 \: and \: x_2 = - 6$

$\sf \bull \: y_1 = 4\: and \: y_2 = - 5$

On substituting the values,

$\sf \longrightarrow \: t = \bigg( \dfrac{7( - 6) + 2( - 7)}{7 + 2} \bigg) \bigg( \dfrac{7( - 5) + 2(4)}{7 + 2} \bigg)$

$\sf \longrightarrow \: \bigg( \dfrac{ - 42 - 14}{9} \bigg) \bigg( \dfrac{ -35 + 8}{9} \bigg)$

$\sf \longrightarrow \: \bigg( \dfrac{ - 56}{9} \bigg) \bigg( \dfrac{ - 27}{9} \bigg)$

$\sf \longrightarrow \: \bigg( \dfrac{ - 56}{9} \bigg) \: - 3$

${ \underline{ \sf {\therefore{The \: coordinates \: of \: point \: {\bf{t}} \: is \: { \bf \: \frac{ - 56}{9} \: - 3}}}}}$

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Note:

If any line segment AB is divided by a point t(x, y) the coordinates of the point t is given by the section formula.

Section formula :

${ \longrightarrow \sf t = \bigg(\dfrac{m_1x_1 + m_2x_2}{m_1 + m_2}\bigg)\bigg(\dfrac{m_1y_1 + m_2y_2}{m_1 + m_2}\bigg) \: }$