Question
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3 : 1 internally.
✓
Answer
Let coordinates of the required point be R(x, y). This means R divides the join of P(4, -3) and Q(8, 5) in the ratio 3:1 internally.Using the Section formula for internal division, here $x_1= 4, y_1= -3, x_2= 8, y_2= 5, m = 3, n = 1$
$\Rightarrow$(x,y) = $\left( \frac { mx _ { 2 } +n x _ { 1 } } { m+n} , \frac { m y _ { 2 } + ny _ { 1 } } { m+n } \right)$
$\Rightarrow$(x,y) = ($\frac { 3 ( 8 ) + 1 ( 4 ) } { 3 + 1 }$,$\frac { 3 ( 5 ) + 1 ( - 3 ) } { 3 + 1 }$)
$\Rightarrow$ (x,y) = $( \frac { 24 + 4 } { 4 } , \frac { 15-3} { 4 })$
$\Rightarrow$ (x,y) = $( \frac { 28 } { 4 } , \frac { 12} { 4 }) =(7, 3)$
$\Rightarrow$ x= 7 and y= 3
Thus, the coordinates of R (x,y) = (7,3)
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