Question

If a semicircle with 'AB' as diameter and having a radius of 5 cm is drawn as shown in below figure then the coordinates of B is___.

• A. (3,0)
• B. (-17,0)
• C. (-2,0)
• D. (-12,0)

Answer 1

The correct option is A

(3,0)

Given coordinates of A=(-7,0) and radius of semicircle =5 cm. From the figure, we can see that B lies an X-axis.

$\therefore$ Let point B =(x,0)

$\because$ length of diameter $2\times$ Radius of circle

$\therefore$ Distance between A and B $=2\times 5$

$\Rightarrow \sqrt{(x-(-7){)}^2}=10$

$\Rightarrow (x+7{)}^2={10}^2$

$\Rightarrow x+7=\pm 10$

$\Rightarrow x+7=10$ (or) x+7=10

$\Rightarrow x=3$ (or) x =-17

$\therefore B=(3,0)$ (or) (-17,0)

From the figure we can see that x-coordinates of B is positive.

$\therefore B=(3,0)$