The coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4) is 
Explanation :
the coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4)
Apply section formula to find coordinates of point Q

Ratio m:n is 2:3 and point R is (x1,y1) , point S is (x2,y2)
Substitute all the values inside the formula

The coordinates of point Q is 
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(a) Using the completing the square method, we need to write into the form of where , so
Expand to find the value of c
Notice that we get back the first two terms, the and the .We need to get rid of the last term of '9' as the term was not in the original form. The final form will look like
Hence,
(b)
(c) , square root both sides plus and minus of 2 Hence
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