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jonny [76]
3 years ago
8

Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8,5) in the ratio 3:1 internall

y.
Mathematics
1 answer:
Inessa05 [86]3 years ago
7 0

Answer:

The coordinates of the point that divides the line internally in the given ratio is (7,3)

Step-by-step explanation:

To find this coordinates, we use the in renal division formula

we have this as;

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

(x1,y1) = (4,-3)

(x2,y2) = (8,5)

(m,n) = (3,1)

So, substituting these values, we have ;

(x,y) = (1(4) + 3)8))/(3 + 1) , (1(-3) + 3)5)/(1 + 3)

(x,y) = (28)/4, (12/4)

(x,y) = (7,3)

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\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{4+10}{2}~,~\cfrac{-6+4}{2} \right)\implies (7,-1) \\\\[-0.35em] \rule{34em}{0.25pt}


\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{origin}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad \stackrel{\textit{midpoint of AB}}{(\stackrel{x_2}{7}~,~\stackrel{y_2}{-1})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(7-0)^2+(-1-0)^2}\implies d=\sqrt{7^2+(-1)^2} \\\\\\ d=\sqrt{48}\implies d\approx 6.93

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