Question

In an examination hall, students are seated at a distance 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 (𝟐, −𝟑), (𝟒,𝟐), and (𝟖, 𝟓) respectively.

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 𝟐 :𝟑. Then what are the coordinates of 𝐈?

• A. $(\frac{28}{5},\frac{26}{5})$
• B. $(\frac{28}{6},\frac{16}{6})$
• C. $(\frac{28}{5},\frac{16}{5})$
• D. $(\frac{18}{5},\frac{16}{5})$

Answer 1

The correct option is C $(\frac{28}{5},\frac{16}{5})$

Let the coordinates of I be (x, y).
Then, by section formula
Dictate and write:
x = [(2×8) + (3×4)]/(2 +3)
x = [16 + 12]/5 = 28/5
And
y = [(2×5) + (3×2)]/(2+3)
y = [10 + 6]/5 = 16/5
Hence, the coordinate of I are $(\frac{28}{5},\frac{16}{5})$.