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

2 : 7

Coordinates of end points are (-6, 10) and (3, -8)

Point that divides the line segment is of coordinates ( -4, 6 )

Lets us consider that , Desired ration = m : n

According to question ,

- 4  = \(\frac{ 3 ×m + n × (-6)}{m + n }\)

-4m -4n = 3m - 6n

2n = 7m

\(\frac{m}{n}\) = \(\frac{2}{7}\)

So, m : n = 2 : 7