Question

Given points (0,0) and (3,6), find the point which partitions the segment into 3:2.

Answer 1

Dividing a number by the ratio 3:2 means dividing into 3+2 = 5 parts

Let (0, 0) be (x₁, y₁) and (3, 6) be (x₂, y₂)

Find one part of the share for each axes, we do
$\frac{x_1+x_2}{5} = \frac{0+3}{5}= \frac{3}{5} =0.6$
$\frac{y_1+y_2}{5}= \frac{0+6}{5}= \frac{6}{5}=1.2$

Then multiplying the one part back into 3: 2, we have
for the x - axis ⇒ (3×0.6) : (2×0.6) = 1.8: 1.2
for the y - axis ⇒ (3×1.2) : (2×1.2) = 3.6: 2.4

The coordinate that divides the segment into 3 parts and 2 parts is (1.8, 3.6)

Correct answer: A