Final answer:
To find all the points on the x-axis that are 17 units away from the point (-2,8), we can use the distance formula. By setting y2 = 0 and solving the equation, we find that the two points on the x-axis are x = 15 and x = -17.
Step-by-step explanation:
To find all the points on the x-axis that are 17 units away from the point (-2,8), we need to consider the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Since we want to find the points on the x-axis, we can set y2 = 0. Plugging in the values into the distance formula, we get:
17 = √((x - (-2))^2 + (0 - 8)^2)
17 = √((x + 2)^2 + 64)
Squaring both sides of the equation, we get:
289 = (x + 2)^2 + 64
225 = (x + 2)^2
Taking the square root of both sides:
15 = x + 2 or -15 = x + 2
Therefore, the two points on the x-axis that are a distance of 17 from the point (-2,8) are x = 15 and x = -17.