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Mathematics · Coordinate Geometry · NCERT Examples

Example 9

A complete, independently verified solution for NCERT Example 9.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 9

section formula · y-axis · ratio of division

Find the ratio in which the y-axis divides the line segment joining A(5, -6) and B(-1, -4). Also find the point of intersection.

Solution

Board-exam working:

Let the y-axis divide AB at P in the ratio k : 1.

By the section formula:

P=(k(−1)+1(5)k+1,k(−4)+1(−6)k+1)P=\left(\frac{k(-1)+1(5)}{k+1},\frac{k(-4)+1(-6)}{k+1}\right)

Since P lies on the y-axis, its x-coordinate is 0.

−k+5k+1=0\frac{-k+5}{k+1}=0
−k+5=0-k+5=0
k=5k=5

Therefore, the ratio is 5 : 1.

Substituting k = 5 in the y-coordinate:

y=5(−4)+1(−6)5+1y=\frac{5(-4)+1(-6)}{5+1}
y=−20−66=−266=−133y=\frac{-20-6}{6}=\frac{-26}{6}=-\frac{13}{3}

Final answer

The ratio is 5 : 1, and the point of intersection is:

(0,−133)\left(0,-\frac{13}{3}\right)