PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoThe section formula is used to get the coordinates of a point by splitting a line segment into two parts with the given ratio.
Let us look at the graph carefully.
From the graph, the line \(AB\) is divided at \(P\) in the ratio \(m : n\).
Therefore, .
So, \(A'P' : P'B'\) is also \(m : n\).
\(n(A'P') =\) \(m(A'B')\)
\(n(x - x_1) =\) \(m(x_2 - x)\)
\(nx - nx_1 = mx_2 - mx\)
\(mx + nx = mx_2 + nx_1\)
\(x(m + n) = mx_2 + nx_1\)
Similarly, .
1. The coordinates of the point \(P(x, y)\) which divides the line segment joining the points \(A(x_1, y_1)\) and \(B(x_2, y_2)\), internally in the ratio \(m : n\) are:
This is known as the section formula.
2. If the point \(P(x, y)\) divides the line segment in the ratio \(k : 1\), then the coordinates are:
3. If the point \(P(x, y)\) divides the line segment in the ratio \(1 : 1\), then the coordinates are:
This is known as the mid-point formula of the line segment.
4. If \(A(x_1, y_1)\), \(B(x_2, y_2)\) and \(C(x_3, y_3)\) be the vertices of a triangle, then the centroid of a triangle is:
Important!
The point at which all the \(3\) medians intersect is a centroid.
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