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Question

Point C is  3/4 of the way from point A(­4, –2) to point B(8, 6). What are the coordinates of C?

Answer 1

The vector AB = (8-4)i +(6-(-2))j= 4i+8j. |AB|=sqrt(4²+8²)=8.944. 3/4 of 8.944= 6.708=|AC|. The angle above the horizontal of |AB|= arctan(8/4)=63.43 degrees. Thus AC = 6.708*cos(63.43)i+6.708*sin(63.43)j= 3i+6j. C is located at x-4=3 and y-(-2)=6 or C(7,4).