Final answer:
The coordinates of point P that divides the line segment with endpoints (-5, 10) and (4, 19) into a 3:1 ratio are (1.75, 16.75).
Step-by-step explanation:
To find the coordinates of point P that divides the line segment with endpoints (-5, 10) and (4, 19) into two parts in a 3:1 ratio, with MP being the longer part, we use the formula for the point that divides a segment in a given ratio:
x = (x1*n + x2)/(m+n)
y = (y1*n + y2)/(m+n)
where (x1, y1) are the coordinates of one endpoint, (x2, y2) are the coordinates of the other endpoint, m:n is the given ratio and x,y are the coordinates of P. Substituting the given values and ratio:
x = (-5*1 + 4*3)/(3+1) = (3*4 - 5)/(4) = (12 - 5)/4 = 7/4 = 1.75
y = (10*1 + 19*3)/(3+1) = (3*19 + 10)/(4) = (57 + 10)/4 = 67/4 = 16.75
Therefore, the coordinates of point P are (1.75, 16.75).