Final answer:
K is the midpoint of overline PQ, K has coordinates (-1, 6) and P has coordinates (-9, -4).The coordinates of Q are (-5, 1)
Step-by-step explanation:
The problem given involves the concept of midpoints in a Cartesian coordinate system. In a coordinate plane, the coordinates of the midpoint M of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2) / 2, (y1 + y2) / 2).
To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the average of the x-coordinates and the average of the y-coordinates.
In this case, the coordinates of P are (-9, -4) and the coordinates of K (the midpoint) are (-1, 6). So we can find the x-coordinate of Q by averaging the x-coordinates of P and K, and find the y-coordinate of Q by averaging the y-coordinates of P and K.
The x-coordinate of Q is: (-9 + (-1))/2 = -10/2 = -5. The y-coordinate of Q is: (-4 + 6)/2 = 2/2 = 1.
Therefore, the coordinates of Q are (-5, 1).
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