Question

The point which divides the line segment joining the points (7,-6) and (3, 4) in ratio 1:2
mternally lies in the​

Answer 1

$x = \frac{mx2 + nx1}{m + n} \\ \\ x = \frac{1 \times 3 + 2 \times 7}{1 + 2} \\ \\ x = \frac{3 + 14}{3} \\ \\ x = \frac{17}{3} \\ \\ y = \frac{my2 + ny1}{m + n} \\ \\ y = \frac{1 \times 4 + 2 \times ( - 6)}{1 + 2} \\ \\ y = \frac{4 - 12}{3} \\ \\ y = \frac{ - 8}{3} \\ \\ \pink{hence} \\ \\ points \: \: \: \: \: are \\ \\ p \: \blue{( \frac{17}{3} \: \: \: \: \: \: \frac{ - 8}{3} )}$

Answer 2

Step-by-step explanation:

Using the section formula, if a point (x,y) divides the line joining the  points (x₁,y₁) and (x₂,y₂) internally in the ratio m:n, then (x,y)=(mx₂+mx₁/m+n, nx₂+nx₁/ m+n₎

substituting (ˣ₁,y₁)= (7,-6) and (x₂.y₂) =(3,4) and m=1 and n=2 in the section formula we get,

the point (1(3)+ 2(7)/1+2,  1(4)+2(-6)/1+2)=(17/3, -8/3)

Since, x− cordinate is positive and y− cordinate is negative, the point lies in the IV quadrant.

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