Question

In an examination hall, students are seated at a distance of 2 m from each other, to maintain the social distance due to CORONA virus pandemic. Let three students sit at points A, B and C whose coordinates are (4, -3), (7,3), and (8, 5) respectively.

Based on the above information, answer the following questions.
(Q) If an invigilator at the point I, lying on the straight line joining B and C such that it divides the distance between them in the ratio of 1 : 2. Then coordinates of I are:

• A. $(\frac{22}{3},\frac{11}{3})$
• B. $(6,1)$
• C. $(\frac{22}{3},\frac{13}{3})$
• D. $(9,1)$

Answer 1

The correct option is A $(\frac{22}{3},\frac{11}{3})$

Here, we will use the section formula.
Let the coordinates of I be (x, y).
Then, by section formula
$\left(\frac{1\times 8+2\times 7}{1+2}\right)$
$=\left(\frac{8+14}{3}\right)$
$x=\left(\frac{22}{3}\right)$
then,
$\left(\frac{1\times 5+2\times 3}{1+2}\right)$
$=\left(\frac{5+6}{3}\right)$
$y=\left(\frac{11}{3}\right)$
Hence, The coordinate of I is $(\frac{22}{3},\frac{11}{3})$.