The vector ab with the end at point b (-2, -6) has coordinates (-4, -15) find the sum of the coordinates of point a.

Given:
vector ab = (-4, -15);
B = (-2, -6).
Find: A = (XA, YA)

Let us determine the coordinates of point A, which is the origin of the vector ab. This is the inverse problem of finding the coordinates of a vector by the coordinates of its start and end points.

X ab = X B – X A;
X A = X B – X ab = – 2 – (-4) = 2.

Y ab = Y B – Y A;
Y A = Y B – Y ab = – 6 – (-15) = 9.

A = (2, 9).

Let’s find the sum of the coordinates of point A:
S = X A + Y A = 2 + 9 = 11.

Answer: point A has coordinates (2, 9), the sum of its coordinates is 11.