Question

The ratio in which the join of points (−2, 5) and (5, −2) is divided by y-axis is ______.

Options

• 3 : 5

• 2 : 5

• 5 : 3

• 5 : 2

Answer 1

The ratio in which the join of points (−2, 5) and (5, −2) is divided by y-axis is 2 : 5.

Explanation:

Any point on \[y\]-axis can be defined as \[(0, y).\]

Let ratio in which the join of points \[(-2, 5)\] and \[(5, -2)\] is divided by \[(0, y)\] be \[k : 1.\]

⇒ \[(0, y) = \left(\frac{k \times 5 + 1 \times -2}{k + 1}, \frac{k \times -2 + 1 \times 5}{k + 1}\right)\]

⇒ \[(0, y) = \left(\frac{5k - 2}{k + 1}, \frac{-2k + 5}{k + 1}\right)\]

⇒ \[0 = \frac{5k - 2}{k + 1}\]

⇒ \[5k - 2 = 0\]

⇒ \[5k = 2\]

⇒ \[k = \frac{2}{5}\]

Substituting value of \[k\] in \[k : 1\], we get:

⇒ \[\frac{2}{5} : 1\]

⇒ 2 : 5