# Ex.7.2 Q9 Coordinate Geometry Solution - NCERT Maths Class 10

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## Question

Find the coordinates of the points which divide the line segment joining $$A \;(-2, 2)$$ and $$B\;(2, 8)$$ into four equal parts.

## Text Solution

Reasoning:

The coordinates of the point $$P(x, y)$$ which divides the line segment joining the points $$A(x1, y1)$$ and $$B(x2, y2)$$, internally, in the ratio $$\rm m1 : m2$$ is given by the Section Formula.

What is the known?

The $$x$$ and $$y$$ co-ordinates of the points $$A$$ and $$B$$.

What is the unknown?

The coordinates of the points which divide the line segment joining $$A \;(-2, 2)$$ and $$B\;(2, 8)$$ into four equal parts.

Steps: From the Figure,

By observation, that points $$P$$, $$Q$$, $$R$$ divides the line segment $$A\; (-2, 2)$$ and $$B \;(2, 8)$$ into four equal parts

Point $$P$$ divides the line segment $$AQ$$ into two equal parts

Hence, Coordinates of

\begin{align} P &= \left( {\frac{{1 \times 2 + 3 \times ( - 2)}}{{1 + 3}},\;\frac{{1 \times 8 + 3 \times 2}}{{1 + 3}}} \right) \\&= \left( { - 1,\;\frac{7}{2}} \right)\end{align}

Point $$Q$$ divides the line segment $$AB$$ into two equal parts

Coordinates of

\begin{align} Q &= \left( {\frac{{2 + ( - 2)}}{2},\;\frac{{2 + 8}}{2}} \right)\\ &= (0,\;5)\end{align}

Point $$R$$ divides the line segment $$BQ$$ into two equal parts

Coordinates of

\begin{align} R &= \,\,\left( {\frac{{3 \times 2 + 1 \times ( - 2)}}{{3 + 1}},\;\frac{{3 \times 8 + 1 \times 2}}{{3 + 1}}} \right)\;\\ &=\left(1, \frac{13}{2}\right)\end{align}

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