Find the cordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally.
Let P(x,y) be the point which divides the line segment internally. Using the section formula for the internal division, i.e.
(x, y) = `(\frac{"m"_{1}"x"_{2}+"m"_{2}"x"_{1}}{"m"_{1}+"m"_{2}},\frac{"m"_{1}"y"_{2}+"m"_{2}"y"_{1}}{"m"_{1}+"m"_{2}})`
Given Us,
`"m"_1` = 3, `"m"_2` = 1
(`"x"_1`,`"y"_1`) = (4, −3)
(`"x"_2`,`"y"_2`) = (8, 5)
Putting the above values in the above formula, we get :
x = `\frac{3(8)+1(4)}{3+1}`, y = `\frac{3(5)+1(-3)}{3+1}`
x = `\frac{24+4}{4}`, y = `\frac{15-3}{4}`
x = `\frac{28}{4}`, y = `\frac{12}{4}`
x = 7, y = 3
Hence, (7,3) is the point which divides the line segment internally.
(x, y) = `(\frac{"m"_{1}"x"_{2}+"m"_{2}"x"_{1}}{"m"_{1}+"m"_{2}},\frac{"m"_{1}"y"_{2}+"m"_{2}"y"_{1}}{"m"_{1}+"m"_{2}})`
Given Us,
`"m"_1` = 3, `"m"_2` = 1
(`"x"_1`,`"y"_1`) = (4, −3)
(`"x"_2`,`"y"_2`) = (8, 5)
Putting the above values in the above formula, we get :
x = `\frac{3(8)+1(4)}{3+1}`, y = `\frac{3(5)+1(-3)}{3+1}`
x = `\frac{24+4}{4}`, y = `\frac{15-3}{4}`
x = `\frac{28}{4}`, y = `\frac{12}{4}`
x = 7, y = 3
Hence, (7,3) is the point which divides the line segment internally.
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