Question

Determine the midpoint of the points where the $x$-intercept is $9$ and the $y$-intercept is $6.$

• A. $(3,\frac{9}{2})$
• B. $(3,-\frac{9}{2})$
• C. $(-\frac{9}{2},3)$
• D. $(\frac{9}{2},3)$

Answer 1

The correct option is D $(\frac{9}{2},3)$

Concept:
The point at which the straight line crosses the $x$-axis is called $x$-intercept.
Hence, at $x=9$, $y=0$.The point is $(9,0)$

The point at which the straight line crosses the $y$-axis is called $y$-intercept.
Hence, at $y=6$, $x=0$.The point is $(0,6)$

Represent these points on the cartesian plane and join them.
The midpoint of the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$(\frac{x_1+y_1}{2},\frac{y_1+y_2}{2})$

$\therefore$ The midpoint of (9, 0) and (0, 6)
$=(\frac{9+0}{2},\frac{0+6}{2})$
$=(\frac{9}{2},\frac{6}{2})$
$=(\frac{9}{2},3)$
or $(4.5,3)$

​​​​​​​Option (d) is correct.