Final answer:
To find the two points of the form (x,-4) that have the same distance of 10 units from the point (3,2), you can use the distance formula and set up an equation.
Step-by-step explanation:
To find the two points of the form (x,-4) that have the same distance of 10 units from the point (3,2), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)^2 + (y2 - y1)^2].
In this case, we have (x1, y1) = (3,2) and (x2, y2) = (x,-4). We want the distance to be 10 units, so we can set up the equation √[(x - 3)^2 + (-4 - 2)^2] = 10. Squaring both sides and simplifying, we get (x - 3)^2 + 36 = 100. Solving for x, we find x = -5 and x = 11.
Therefore, the two points of the form (x, -4) that have the same distance of 10 units from the point (3,2) are (-5, -4) and (11, -4). So the correct answer is A. (-5, -4) and (11, -4).