Gujarat BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
Question
In what ratio does the point $(-4, 6)$ divide the line segment joining the points $A(-6, 10)$ and $B(3, -8)$?
✓
Answer
Let $(-4, 6)$ divide $AB$ internally in the ratio $k:1$. Using the section formula, we get
$( - 4,6 ) = \left( \frac { 3 k - 6 } { k + 1 } , \frac { - 8 k + 10 } { k + 1 } \right)$
So, $- 4 = \frac { 3 k - 6 } { k + 1 }$
$i.e., -4k - 4 = 3k - 6$
$i.e., 7k = 2$
$i.e., k:1 = 2:7$
The same can be checked for the y-coordinate also.
Therefore, the ratio in which the point $(-4,6)$ divides the line segment $AB$ is $2: 7$.
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