Mathematics: Given the points m (-3,-4) and t (5,0), find the coordinates of the point q on direct line segment mt that partitions mt in the ratio 2: 3. write the coordinates of the point q in decimal form.

Ten thousandsStep-by-step explanation:...

Given the points m (-3,-4) and t (5,0), find the coordinates

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15.03.2022

The coordinates of the point Q = (x,y) =(0.2,-2.4)

Step-by-step explanation:

The section formula, (x,y) is the coordinate on line joining two points (x_1,y_1) , (x_2,y_2) in the ratio of m is to n.

$x=\frac{x_1\times n+x_2\times m}{m+n}$

$y=\frac{y_1\times n+y_2\times m}{m+n}$

Given the points M (-3,-4) and T (5,0) , on this line joining these point there was another point Q which divides into ratio of 2:3.

(x_1,y_1) , (x_2,y_2)=(-3,-4) , (5,0)

The coordinates of the point Q = (x,y)

m = 2 , n = 3

$x=\frac{-3\times 3+5\times 2}{2+3}$

$x=\frac{1}{5}=0.2$

$y=\frac{-4\times 3+0\times 2}{2+3}$

$y=\frac{-12}{5}=-2.4$

The coordinates of the point Q = (x,y) = $(\frac{1}{5},\frac{-12}{5})=(0.2,-2.4)$

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