Question

The points on X-axis at a distance of 10 units from (11, –8) are

• A. (5, 0) and (16, 0)
• B. (6, 0) and (17, 0)
• C. (5, 0) and (17, 0)
• D. (5, 2) and (17, 0)

Answer 1

The correct option is C (5, 0) and (17, 0)

We know that y-coordinate of a point on X-axis is always 0.

Therefore, the required points can be expressed in the form (x, 0) where x is the x-coordinate.

Distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

Distance between (11, -8) and (x, 0) = 10 units (given)

$\Rightarrow (x-11{)}^2+8^2={10}^2$
$\Rightarrow x^2-22x+121+64=100$
$\Rightarrow x^2-22x+85=0$

On factorising the above equation, we get
$x^2-17x-5x+85=0$
$\Rightarrow (x-17)(x-5)=0$
$\Rightarrow x=17or5$

Hence, the required points are (17, 0) and (5, 0).