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Mathematics · Coordinate Geometry · NCERT Examples

Example 8

A complete, independently verified solution for NCERT Example 8.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 8

section formula · trisection · internal division

Find the coordinates of the points of trisection of the line segment joining A(2, -2) and B(-7, 4).

Line segment AB from A(2, -2) to B(-7, 4), divided into three equal parts by P and Q.
Figure 7-11 from the supplied NCERT chapter.

Solution

Board-exam working:

Let P and Q be the trisection points, so AP = PQ = QB.

Point P divides AB internally in the ratio 1 : 2.

P=(1(−7)+2(2)1+2,1(4)+2(−2)1+2)P=\left(\frac{1(-7)+2(2)}{1+2},\frac{1(4)+2(-2)}{1+2}\right)
P=(−7+43,4−43)=(−1,0)P=\left(\frac{-7+4}{3},\frac{4-4}{3}\right)=(-1,0)

Point Q divides AB internally in the ratio 2 : 1.

Q=(2(−7)+1(2)2+1,2(4)+1(−2)2+1)Q=\left(\frac{2(-7)+1(2)}{2+1},\frac{2(4)+1(-2)}{2+1}\right)
Q=(−14+23,8−23)=(−4,2)Q=\left(\frac{-14+2}{3},\frac{8-2}{3}\right)=(-4,2)

Final answer

The points of trisection are (-1, 0) and (-4, 2).