Final answer:
To find point P that is 3/4 of the way from M(-5, 8) to N(3, 0), the formula P = (1-t)M + tN is used, and the coordinates are calculated to be (1, 4).
Step-by-step explanation:
To find the coordinates of point P that is 3/4 of the distance from point M(-5, 8) to point N(3, 0), you can use the formula for finding a point that is a certain fraction of the way from one point to another on a line. This can be done using the formula P = (1-t)M + tN where M and N are the coordinates of the points and t is the fraction of the distance from M to N.
By substituting the values we have:
For the x-coordinate:
Px = (1-3/4)(-5) + (3/4)(3) = (-5 + 15/4) + (9/4) = (-20/4 + 15/4) + (9/4) = 4/4 = 1
For the y-coordinate:
Py = (1-3/4)(8) + (3/4)(0) = (2/4)(8) = 8/2 = 4
Therefore, the coordinates of point P are (1, 4).