Question

Find points on the x axis each of which is at a distance of 10 units from the point a 11 8

Answer 1

Answer:

Step-by-step explanation:

At the x axis, the y coordinate is zero. Hence, any point on the x axis has a coordinate (x,0).

Now, this point is at a distance of 10 units from the point a(11,-8)

The distance formula is given by

$d=\sqrt{(x_{2}-x_{1} )^{2}-(y_{2}-y_{1})^{2}    } \\10=\sqrt{(11-x)^{2}+(-8-0)^2 }$

Squaring both sides, we get

$100=(11-x)^2+(-8-0)^2\\100=121+x^2-22x+64\\x^2-22x+85=0\\x^2-17x-5x+85=0\\x(x-17)-5(x-17)=0\\(x-17)(x-5)=0\\x=5,17$

Therefore, the points are (5,0) and (17,0)