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Mathematics · Coordinate Geometry · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 3

distance formula · collinear points · classroom grid

Figure 7.6 shows Ashima, Bharti and Camella seated at A(3, 1), B(6, 4) and C(8, 6). Are they seated in a line? Give reasons.

A ten-by-ten classroom coordinate grid showing Ashima at A(3, 1), Bharti at B(6, 4), and Camella at C(8, 6).
Figure 7-6 from the supplied NCERT chapter.

Solution

Board-exam working:

Using the distance formula:

AB=(6−3)2+(4−1)2=9+9=32AB=\sqrt{(6-3)^2+(4-1)^2}=\sqrt{9+9}=3\sqrt2
BC=(8−6)2+(6−4)2=4+4=22BC=\sqrt{(8-6)^2+(6-4)^2}=\sqrt{4+4}=2\sqrt2
AC=(8−3)2+(6−1)2=25+25=52AC=\sqrt{(8-3)^2+(6-1)^2}=\sqrt{25+25}=5\sqrt2

Now compare the distances:

AB+BC=32+22=52=ACAB+BC=3\sqrt2+2\sqrt2=5\sqrt2=AC

Since AB + BC = AC, point B lies between A and C. Therefore, A, B and C are collinear.

Final answer

Yes. Ashima, Bharti and Camella are seated in a straight line.