Final answer:
To find point c which is 1/5 the distance from point a to point b, calculate the distance between a and b using the distance formula. Multiply the distance by 1/5 and add it to the coordinates of point a.
Step-by-step explanation:
To find point c which is 1/5 the distance from point a to point b, we first need to calculate the distance between a and b. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the values for point a (1, 10) and point b (7, 1), we can substitute these values into the distance formula to find the distance between a and b. Once we have the distance, we can then calculate point c by multiplying the distance by 1/5 and adding it to the coordinates of point a.