Question

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

Answer 1

• ❍ Let AB be the line segment, with co – ordinates A(–2, 2) and point B(2, 8). And, x, y and z points are dividing the line segment AB, into four equal parts respectively.

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M I D – P O I N T :

• We'll use Mid – point formula, this formula is use to calculate the co – ordinates of points which divides the line segment. And, the Mid – point formula is given by :

$\bf{\dag}\;\;\boxed{\sf{\bigg(\dfrac{x_1 + x_2}{2},\;\dfrac{y_1 + y_2}{2}\bigg)}}$

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The mid dividing point is 'y'. So, the co – ordinates of y :

$\begin{gathered}:\implies\sf\bigg(\dfrac{-2 + 2}{2}, \;\dfrac{2 + 8}{2}\bigg) \\\\\\:\implies\sf \bigg(\dfrac{0}{2}, \;\cancel\dfrac{10}{2} \bigg) \\\\\\:\implies{\underline{\boxed{\frak{\Big(0, 5\Big)}}}}\end{gathered}$

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• And Now, co – ordinates of point 'x' :

$\begin{gathered}:\implies\sf \bigg(\dfrac{-2 + 0}{\;2},\; \dfrac{2+5}{2}\bigg) \\\\\\:\implies\sf \bigg(\cancel\dfrac{-2}{\;2},\; \dfrac{7}{2}\bigg) \\\\\\:\implies{\underline{\boxed{\frak{\Big(-1,\;\dfrac{7}{2}\bigg)}}}}\end{gathered}$

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Similarly, co – ordinates of point 'z' :

$\begin{gathered}:\implies\sf \bigg(\dfrac{0 +2}{2},\;\dfrac{5+8}{2}\bigg) \\\\\\:\implies\sf \bigg(\dfrac{2}{2}, \dfrac{13}{2} \bigg) \\\\\\:\implies{\underline{\boxed{\frak{\bigg(1,\;\dfrac{13}{2}\bigg)}}}}\end{gathered}$

$\therefore{\underline{\sf{Hence,\;the\; coordinates \;of\; dividing\; points\;are\; \bf{(0,5)\;,\bigg(-1,\;\dfrac{7}{2}\bigg)\;\&\;\bigg(1,\dfrac{13}{2}\bigg)}.}}}$

Answer 2

The dividing points are (0,5), (-1,1/2) & 1,13/2).