Question

The mid-point of the line segment joining the points (5, 4) and (6, 4) lies on ______.

Options

• x-axis

• y-axis

• origin

• neither x-axis nor y-axis

Answer 1

The mid-point of the line segment joining the points (5, 4) and (6, 4) lies on neither x-axis nor y-axis.

Explanation:

Given:

x₁ = 5, y₁ = 4

x₂ = 6, y₂ = 4

The midpoint of a line segment joining (x₁, y₁) and (x₂, y₂).

Using the midpoint formula:

M = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

= `((5 + 6)/2, (4 + 4)/2)`

= `((11)/2, (8)/2)`

= (5.5, 4)

x-axis: For a point to lie on the x-axis, its y-coordinate must be 0 (e.g., (5.5, 0)). Here, y = 4.

y-axis: For a point to lie on the y-axis, its x-coordinate must be 0 (e.g., (0, 4)). Here, x = 5.5.

Origin: For a point to be at the origin, both coordinates must be 0 (0, 0).