Final answer:
To find the length of PQ, use the distance formula and substitute the coordinates of P and Q. Then round your answer to the nearest tenth. To find the coordinates of the midpoint of PQ, use the midpoint formula and substitute the coordinates of P and Q.
Step-by-step explanation:
To find the length of PQ, we can use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Given that P is located at (2, 6) and Q is located at (-6, 1), we can substitute these coordinates into the formula: d = sqrt((-6 - 2)^2 + (1 - 6)^2). Simplifying the equation, we get d = sqrt((-8)^2 + (-5)^2) = sqrt(64 + 25) = sqrt(89). Rounding to the nearest tenth, PQ is approximately 9.4 units long.
To find the coordinates of the midpoint of PQ, we can use the midpoint formula: (x, y) = ((x1 + x2)/2, (y1 + y2)/2). Substituting the coordinates of P and Q into the formula, we get (x, y) = ((2 - 6)/2, (6 + 1)/2). Simplifying, we get (x, y) = (-2/2, 7/2) = (-1, 3.5). Therefore, the coordinates of the midpoint of PQ are (-1, 3.5).