Question

What are the coordinates of the point on the directed line segment from (-8, 5)(−8,5) to (4, -3)(4,−3) that partitions the segment into a ratio of 5 to 3?

Answer 1

(2, -7/2)

Explanation:

According to the midpoint theorem;

M(X, Y) = [(ax1+bx2/a+b), ay1+by2/a+b ]

(x1, y1) and (x2, y2) are the coordinates

a:b is the given ratio

Given the following

Coordinate of the line segment (-8, 5) and (4, -3)

Ratio: 5:3

Get the X coordinate;

X = ax1 + bx2 / a+b

X = 5(-8) + 3(4)/5+3

X = -40+12/8

X = -28/8

X = -7/2

Get the Y coordinate

Y = ay1 + by2 / a+b

Y = 5(5) + 3(-3)/5+3

Y = 25-9/8

Y = 16/8

Y = 2

Hence the required coordinate is (2, -7/2)