Final answer:
To find the points on the line y = 3 that are 10 units from (3, -3), we can use the distance formula. The two points are (11, 3) and (-5, 3).
Step-by-step explanation:
To find the points on the line y = 3 that are 10 units from (3, -3), we can use the distance formula. Let's call the x-coordinate of the points we're looking for as x. The distance formula is given by:
d = sqrt((x - 3)^2 + (3 - (-3))^2)
Substituting the values into the formula, we have:
10 = sqrt((x - 3)^2 + 36)
Squaring both sides of the equation:
100 = (x - 3)^2 + 36
Expanding and simplifying:
64 = (x - 3)^2
Taking the square root of both sides:
x - 3 = ±8
Solving for x:
x = 11 or x = -5
Therefore, the two points on the line y = 3 that are 10 units from (3, -3) are (11, 3) and (-5, 3).