Question

Example 7: In what ratio does the point (-4, 6) divide the line segment joining the points A(-6,10) and B (3,-8)​

Answer 1

Question :-

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

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$\boxed{ \bf \: solution}$

note :- using Alternate Method

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let point p(-4,6) divides the line segment joining the points at A(-6,10) and B(3,-8) in the ratio K:1

By using section formula , we get

$\bf \: (4,6) = ( \frac{3 \times k + ( - 6) \times 1}{k + 1} ), \frac{ - 8 \times k + 10 \times 1}{k + 1} \\ \bf \: ( - 4,6) = ( \frac{3k - 6}{k + 1} , \frac{ - 8k + 10}{k + 1} )...(1)$

on equating X - coordinate from both sides of Eq.(1) we get

$\bf \: - 4 = \frac{3k - 6}{k + 1} \\ \bf \: = > - 4(k + 1) = 3k - 6 = - 4k - 4 = 3k - 6 \\ \bf \: = 3k + 4k = 6 - 4 = > 7k = 2 = > k = \frac{2}{7} ....(2)$

Verification on equality Y - coordinate from both sides of Eq.(1) , we get

$\bf \: 6 = \frac{ - 8k + 10}{k + 1} \\ \bf \: on \: pulling \: k = \frac{2}{7} from \: eq.(2)we \: get$

$\bf \: 6 = \frac{ \frac{ - 8 \times 2 + 10}{7} }{ \frac{2}{7} + 1} = > 6 = \frac{ - 16 + 70}{2 + 7} = \frac{54}{9} = 6$

hence , the point (-4,6) divides the line segment joining the point A(-6,10) and B(3,-8) in the ratio 2:7

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$\boxed{\bf\:Answer => ratio = 2:7}$

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Extra information ★

• The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis.