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)=(m+nmx2​+nx1​​,m+nmy2​+ny1​​)


Substituting (x1​,y1​)=(7,−6) and (x2​,y2​)=(3,4)  and m=1,n=2 in the section formula, we get

the point (1+21(3)+2(7)​,1+21(4)+2(−6)​)=(317​,3−8​)


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

To find the point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally, we can use the section formula. The section formula is used to find the coordinates of a point that divides a line segment into a given ratio.



The section formula states that the coordinates (x, y) of a point P which divides the line segment joining two points (x₁, y₁) and (x₂, y₂) in the ratio m:n internally can be found using the following formula:

x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)

where m and n are the ratio in which the line segment is divided.



In this case, the coordinates of the two given points are (7, -6) and (3, 4) and the ratio in which the line segment is divided internally is 1:2. Therefore, m = 1 and n = 2.

Using the section formula, we can find the coordinates of the point P that divides the line segment internally.

x = (1 * 3 + 2 * 7) / (1 + 2) = (3 + 14) / 3 = 17 / 3
y = (1 * 4 + 2 * -6) / (1 + 2) = (4 - 12) / 3 = -8 / 3

So, the coordinates of the point P are (17/3, -8/3).



The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally lies at (17/3, -8/3).