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Mathematics · Coordinate Geometry · NCERT Examples

Example 7

A complete, independently verified solution for NCERT Example 7.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 7

section formula · ratio of division · coordinate comparison

In what ratio does P(-4, 6) divide the line segment joining A(-6, 10) and B(3, -8)?

Solution

Board-exam working:

Let P divide AB internally in the ratio m₁ : m₂.

Using the x-coordinate in the section formula:

−4=3m1−6m2m1+m2-4=\frac{3m_1-6m_2}{m_1+m_2}

Cross multiplying:

−4m1−4m2=3m1−6m2-4m_1-4m_2=3m_1-6m_2
2m2=7m12m_2=7m_1
m1m2=27\frac{m_1}{m_2}=\frac27
m1:m2=2:7m_1:m_2=2:7

Verification using the y-coordinate:

y=2(−8)+7(10)2+7y=\frac{2(-8)+7(10)}{2+7}
y=−16+709=549=6y=\frac{-16+70}{9}=\frac{54}{9}=6

The y-coordinate agrees with P(-4, 6).

Final answer

The point divides the line segment internally in the ratio 2 : 7.