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 three section formula, we get
$(-4,6)=\Big(\frac{3\text{k}-6}{\text{k}+1},\frac{-8\text{k}+10}{\text{k}+1}\Big)$
So, $-4=\frac{3\text{k}-6}{\text{k}+1}$
i.e.,$ -4k - 4 = 3k - 6$
i.e., $7k = 2$
i.e., $k : 1 = 2 : 7$
You check for the y-coordinate also, So, the point $(-4, 6)$ divides the line segment joining the points $A(-6, 10)$ and $B(3, -8)$ in the ratio $2 : 7.$
Divide AB internally in the ratio $k : 1$ using three section formula, we get
$(-4,6)=\Big(\frac{3\text{k}-6}{\text{k}+1},\frac{-8\text{k}+10}{\text{k}+1}\Big)$
So, $-4=\frac{3\text{k}-6}{\text{k}+1}$
i.e.,$ -4k - 4 = 3k - 6$
i.e., $7k = 2$
i.e., $k : 1 = 2 : 7$
You check for the y-coordinate also, So, the point $(-4, 6)$ divides the line segment joining the points $A(-6, 10)$ and $B(3, -8)$ in the ratio $2 : 7.$
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