Final answer:
The coordinates of the point that divides the line segment between (-1, 6) and (3, -2) in the ratio of 5 to 3 is found using the section formula and the result is (1.5, 1).
Step-by-step explanation:
The task is to find the coordinates of a point on the line segment that divides the segment in a 5 to 3 ratio. To do this, we use the section formula in coordinate geometry, which is an application of the concept of similar triangles or weighted averages.
The section formula for a line segment with endpoints A(x1, y1) and B(x2, y2), divided in the ratio m:n internally, is given by:
( (mx2 + nx1)/(m+n) , (my2 + ny1)/(m+n) )
In this case, point A is (-1, 6), point B is (3, -2), and the ratio m:n is 5:3. Inserting these values into the section formula, we get:
( (5*3 + 3*(-1))/(5+3) , (5*(-2) + 3*6)/(5+3) ) = ( (15 - 3)/8 , (-10 + 18)/8 ) = ( 12/8 , 8/8 ) = ( 1.5 , 1 ).
So the coordinates of the point on the line segment that divides it into the ratio of 5 to 3 is (1.5, 1).