Final answer:
To find the coordinates of the point 2/3 of the way from P to Q (-5, 4) and Q (7, -5), we use the formulas x = (2/3)(Qx - Px) + Px and y = (2/3)(Qy - Py) + Py. Plugging in the values, we find that the coordinates of the point are (3, -2).
Step-by-step explanation:
To find the coordinates of a point that is 2/3 of the way from P to Q, we need to calculate the x and y coordinates separately.
For the x-coordinate, we use the formula: x = (2/3)(Qx - Px) + Px. Plugging in the values, we get: x = (2/3)(7 - (-5)) + (-5) = (2/3)(12) - 5 = 8 - 5 = 3.
For the y-coordinate, we use the formula: y = (2/3)(Qy - Py) + Py. Plugging in the values, we get: y = (2/3)(-5 - 4) + 4 = (2/3)(-9) + 4 = -6 + 4 = -2.
Therefore, the coordinates of the point 2/3 of the way from P to Q are (3, -2).