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 $R (x,y) = (7,3)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?
Find the value of $k$ for which each of the following system of equations have infinitely many solutions:
→$2x + 3y = 7$
$(k + 1)x + (2k - 1)y = 4k + 1$
If $D$ and $E$ are points on sides $AB$ and $AC$ respectively of a $∆ABC$ such that $DE || BC$ and $BD = CE.$ Prove that $\triangle\text{ABC}$ is isosceles.
→A plot is in the form of a rectangle $ABCD$ having semi-circle on $BC$ as shown in the following figure. If $AB = 60\ m$ and $BC = 28\ m,$ find the area of the plot.
→The radii of the circular ends of a frustum of height $6\ cm$ are $1\ cm$ and $6\ cm,$ respectively. Find the slant height of the frustum.
→In the figure, $E$ is the point on side $CB$ produced on an isosceles triangle $ABC$ with $AB = AC.$ If $AD \bot BC$ and $EF \bot AC,$ prove that $\triangle ABD \sim \triangle ECF.$
→In $\triangle\text{ABC},\ \angle\text{A}=60^\circ.$ Prove that $B C^2=A B^2+A C^2-A B \times A C$.
→Write a quadratic polynomial, sum of whose zeros is $2\sqrt{3}$ and their product is $2.$
→In $\triangle A B C$, right angled at B, if $\tan A = \frac { 1 } { \sqrt { 3 } }$. Find the value of sin $A \cos C + \cos A \sin C.$
→If $\frac{4}{5}, a, 2$ are three consecutive terms of an $A.P.?$
→