What are the coordinates of the point on the directed line segment from(−3,−9) to (9,7) that partitions the segment into a ratio of 5 to 3?

Question

graph

Answer 1

here is different method

x_5/8=-3+(5/8)(9-(-3))=9/2

y_5/8=-9+(5/8)(7-(-9))=1

Answer 2

Let this point is (x, y) Then (x + 3)/((9 - x) = 5/3 and (y + 9)/(7 - y) = 5/3;

3x + 9 = 45 - 5x; 8x = 36, x = 9/2;

3y + 27 = 35 - 5y, 8y = 8, y = 1.

Point is (9/2, 1)