Final answer:
To find points that are equidistant from P(2,6) and Q(-4,0), first find the midpoint between the two given points. Then write the equation of the points that are equidistant from the midpoint.
Step-by-step explanation:
To find points that are equidistant from two given points, we can find the midpoint between the two given points. The equation of the points equidistant from P(2,6) and Q(-4,0) will be the set of all points that are equidistant to the midpoint.
Step 1: Find the midpoint using the formula: midpoint = ((x1 + x2)/2, (y1 + y2)/2)
midpoint = ((2 + (-4))/2, (6 + 0)/2) = (-1, 3)
Step 2: Write the equation for the points equidistant from the midpoint. Since the distance is the same from the midpoint to any point equidistant, the equation will be x = -1 (horizontal line passing through (-1, 3)).