Question

select the point(s) that satisfy the condition. two points on the x - axis that are 10 units from (1,8)

Explanation:

Step1: Recall the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Points on the $x$-axis have the form $(x,0)$. Let $(x_1,y_1)=(x,0)$ and $(x_2,y_2)=(1,8)$, and $d = 10$. Then $10=\sqrt{(x - 1)^2+(0 - 8)^2}$.

Step2: Square both sides of the equation

Squaring both sides gives $100=(x - 1)^2+64$.

Step3: Simplify the equation

Subtract 64 from both sides: $(x - 1)^2=100 - 64=36$.

Step4: Solve for $x$

Take the square - root of both sides: $x - 1=\pm6$.

• Case 1: When $x - 1 = 6$, then $x=7$.
• Case 2: When $x - 1=-6$, then $x=-5$.

Answer:

The points are $(-5,0)$ and $(7,0)$