Question

The line represented by ${\displaystyle \frac{x}{4}+\frac{y}{6}=1}$, intersects the x-axis and y-axis, respectively, at P and Q. The coordinates of the mid-point of line segment PQ are ______.

विकल्प

• (2, 3)

• (3, 2)

• (2, 0)

• (0, 3)

Answer 1

The line represented by ${\displaystyle \frac{x}{4}+\frac{y}{6}=1}$, 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:

${\displaystyle \frac{x}{4}+\frac{y}{6}=1}$

For the x-intercept, set y = 0:

${\displaystyle \frac{x}{4}+\frac{0}{6}=1}$

${\displaystyle \frac{x}{4}=1}$

x = 4

So, P = (4, 0). 

For the y-intercept, set x = 0:

${\displaystyle \frac{0}{4}+\frac{y}{6}=1}$

${\displaystyle \frac{y}{6}=1}$

y = 6

So, Q = (0, 6).

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

${\displaystyle M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})}$

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

${\displaystyle M=(\frac{4+0}{2},\frac{0+6}{2})}$

${\displaystyle M=(\frac{4}{2},\frac{6}{2})}$

M = (2, 3)