Question

Point P is shown graphed on the coordinate grid as (6,4). In relation to point P, point A is located 2 units closer to the origin along the x-axis and 2 units farther from it along the y-axis. What would be the location of point A ?

Answer 1

Answer:

The coordinates of point A are $A(x,y) = (4,6)$.

Step-by-step explanation:

The location of point A is defined by the vectorial sum of absolute coordinates of point P and coordinates of point A relative to coordinates of point P, that is:

$A(x,y) = P(x,y) + \vec v_{PA}$ (1)

$P(x,y)$ - Absolute coordinates of point P.

$A(x,y)$ - Absolute coordinates of point A.

$\vec v_{PA}$ - Vector to point A relative to point P.

If we know that $P(x,y) =(6,4)$ and $\vec v_{PA} = (-2, 2 )$, then the absolute coordinates of point A are:

$A(x,y) = (6,4) +(-2,2)$

$A(x,y) = (4,6)$

The coordinates of point A are $A(x,y) = (4,6)$.