Question

Prove that the line through (0, 0) and (2, 3) is parallel to the line through (2, −2) and (6, 4).

Answer 1

⇒ The first line passes through points (0, 0) and (2, 3),

Using the slope formula:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m_1 = (3 - 0)/(2 - 0)`

∴ `m_1 = 3/2`

⇒ The second line passes through points (2, −2) and (6, 4),

Using the slope formula:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m_2 = (4 - (-2))/(6 - 2)`

`m_2 = (4 + 2)/4`

`m_2 = 6/4`

∴ `m_2 = 3/2`

Since the slopes of both lines are equal `(m_1 = m_2 = 3/2)`, the line passing through (0, 0) and (2, 3) is parallel to the line passing through (2, −2) and (6, 4).

Hence Proved.