Final answer:
The midpoint of the segment ST with endpoints S(-6,1) and T (-6,-1) is (-6, 0). For the midpoint to lie on the line y = -x, its y-coordinate would need to be 6, not 0. Therefore, the statement is false. The correct answer is B. False, the midpoint M does not lie on the line y = -x.
Step-by-step explanation:
To determine if the statement "If ST has endpoints S(-6,1) and T (-6,-1), then the midpoint M of ST lies on the line (y= -x)." is true or false, we need to calculate the midpoint M of the segment ST. The midpoint formula is:
M = ((x1 + x2)/2, (y1 + y2)/2)
Using the coordinates of S(-6, 1) and T(-6, -1), we find:
M = ((-6 - 6)/2, (1 - 1)/2) = (-6, 0)
The midpoint M is the point (-6, 0). For a point to lie on the line y = -x, its coordinates must satisfy this equation. Plugging the x-coordinate of the midpoint into this equation we get y = -(-6) = 6, which does not equal the y-coordinate of the midpoint (0). Therefore, the midpoint M does not satisfy the equation y = -x.
The correct answer is B. False, the midpoint M does not lie on the line y = -x.