Question

The endpoints of directed line segment PQ have coordinates of P (-7, -5) and Q (5, 3). What are the coordinates of point A, on segment PQ, that divide segment PQ into a ratio of 1:3?

Answer 1

(2,1)

Explanation:

The coordinate point between two points divided between ratio a and b is expressed as;

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

Given the coordinate points (-7,-5) and (5,3) divided within the ratio 1:3

X = ax1+bx2/a+b

X = 1(-7)+3(5)/1+3

X = -7+15/4

X = 8/4

X = 3

Similarly

Y = ay1+by2/a+b

Y = 1(-5)+3(3)/1+3

Y = -5+9/4

Y = 4/4

Y = 1

Hence the required coordinate point is (2,1)