Question

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6) (or) Find the roots of quadratic equation 3x² - 2√6 x + 2 = 0​

Answer 1

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then 

(x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Let the point P(−1,6) divides the line joining A(−3,10) and (6,−8) in the ratio k:1

Then, by section formula,

the coordinates of P are (k+16k−3,k+1−8k+10)

⇒(−1,6)=(k+16k−3,k+1−8k+10)

∴k+16k−3=−1⇒6k−3=−k−1⇒6k+k=3−1⇒7k=2∴ k=2/7