Question

Find the coordinates of the points which divide the line segment joining the points $(-4,0)$ and $(0,6)$ in $4$ equal parts.

• A. $\left(\begin{array}{c}-3,\frac{3}{2}\end{array}\right)$
• B. $(-2,3)$,
• C. $\left(\begin{array}{c}-1,\frac{9}{2}\end{array}\right)$
• D. All of the above

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $\left(\begin{array}{c}-3,\frac{3}{2}\end{array}\right)$
B $(-2,3)$,
C $\left(\begin{array}{c}-1,\frac{9}{2}\end{array}\right)$
D All of the above

Given-

$A(-4,0)$ & $B(0,6)$ are the end points of the line segment AB.

To find out-

The coordinates of the points which divide AB into 4 equal segments.

Solution

If the line AB is divided into 4 segments then there will be 3 points $p,q$ & $r$ such that $Ap=pq=qr=Bq$.

Then, $q$ is the mid point of AB.

$p$ is the mid point of $Aq,$ and $r$ is the mid point of $Bq.$

We shall apply mid point formula

$(X,Y)=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}).$

${AB}_M=q=(\frac{-4-0}{2},\frac{0-6}{2})=(-2,-3).$

${Aq}_M=p=(\frac{-4-2}{2},\frac{0+3}{2})=(-3,\frac{3}{2}),$

${Bq}_M=r=(\frac{-2+0}{2},\frac{3+6}{2})=(-1,\frac{9}{2}).$