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Mathematics · Coordinate Geometry · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 6

section formula · internal division · ratio

Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) internally in the ratio 3 : 1.

Solution

Board-exam working:

Let A(4, -3), B(8, 5), and let P(x, y) divide AB in the ratio 3 : 1.

Using the section formula:

x=3(8)+1(4)3+1x=\frac{3(8)+1(4)}{3+1}
x=24+44=284=7x=\frac{24+4}{4}=\frac{28}{4}=7
y=3(5)+1(−3)3+1y=\frac{3(5)+1(-3)}{3+1}
y=15−34=124=3y=\frac{15-3}{4}=\frac{12}{4}=3

Final answer

The required point is (7, 3).