Question

The line represented by `x/4 + y/6 = 1`, intersects the x-axis and y-axis, respectively, at P and Q. The coordinates of the mid-point of line segment PQ are ______.

Options

• (2, 3)

• (3, 2)

• (2, 0)

• (0, 3)

Answer 1

The line represented by `x/4 + y/6 = 1`, intersects the x-axis and y-axis, respectively, at P and Q. The coordinates of the mid-point of line segment PQ are (2, 3).

Explanation:

The given equation is:

`x/4 + y/6 = 1`

For the x-intercept, set y = 0:

`x/4 + 0/6 = 1`

`x/4 = 1`

x = 4

So, P = (4, 0). 

For the y-intercept, set x = 0:

`0/4 + y/6 = 1`

`y/6 = 1`

y = 6

So, Q = (0, 6).

The midpoint M of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

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

Substituting P(4,0) and Q(0,6):

`M = ((4 + 0)/2, (0 + 6)/2)`

`M = (4/2, 6/2)`

M = (2, 3)