Final answer:
Point P on line MP, where P is 1/3 the distance from M(-3, -4) to N(1.5, 2.5), is calculated using a specific formula and the coordinates of point P are (-0.75, -0.75). However, this result does not match any of the provided options, suggesting an error.
Step-by-step explanation:
To find point P on line MP where P is 1/3 the distance from M(-3, -4) to N(1.5, 2.5), we can use the formula for determining a point that divides a line segment into a given ratio. In this case, the ratio is 1:2 since P is 1/3 the way from M to N.
The formula is given by:
- Px = (x1 + rx2) / (1 + r)
- Py = (y1 + ry2) / (1 + r)
Where r is the ratio, x1 and y1 are the coordinates of point M, and x2 and y2 are the coordinates of point N.
Substituting the given values:
- Px = (-3 + 1(1.5)) / (1 + 1) = (-1.5) / 2 = -0.75
- Py = (-4 + 1(2.5)) / (1 + 1) = (-1.5) / 2 = -0.75
Thus, the coordinates of point P are (-0.75, -0.75), which is not one of the provided options. It looks like there may have been an error in the choices given by the question or in the calculation.