Answer:
Segment Ratio Formula: The coordinates of the point that splits a segment into an arbitrary ratio, n:m, or fractional part, n ⁄ (n+m) , are given by:
x = [n ⁄ (n+m)] (x2 - x1) + x1 and y = [n ⁄ (n+m)] (y2 - y1) + y1
Where [n ⁄ (n+m)] is the desired distance ratio from the starting point, both n and m are positive integers, and ( x1, y1) are the coordinates of one end point and ( x2, y2) are the coordinates of the other endpoint.
For this problem, n = 3 and m = 1 since (3 ⁄ (3+1) = 3 ⁄ 4, ( x1, y1) = (-5, -4) and ( x2, y2) = (-3,3)
x = [n ⁄ (n+m)] (x2 - x1) + x1 = {(3 ⁄ 4)*[ (-3 )- (-5) ]} + (-5) = [(3/4)*(2)] - 5 = [3/2] - 10/3 = -7 ⁄ 2
y = [n ⁄ (n+m)] (y2 - y1) + y1 ={ (3/4)*[3 - (- 4)] } + (-5) = [(3/4) (7) ] - 5 = [21/4] - [20/4] = 1 ⁄ 4
The coordinates of the point are ( -7/2 , 1/4)
Step-by-step explanation:
