Question

point P lies on the origin of a coordinate system. if you translate the point 5 units up, then 4 units left, then 4 units down, the result is point P. what are the coordinates of point P

Answer 1

The coordinates of point P after all the translations become: (-4, 1)

Explanation:

The point P lies on the origin of a coordinate system.

i.e. P(0, 0)

Translating point 5 units up will translate the coordinates from (0, 0) to :

(x, y) → (x, y+5)

(0, 0) → (0, 0+5) = (0, 5)

THEN

Translating point 4 units left will translate the coordinates from (0, 5) to :

(x, y) → (x-4, y)

(0, 5) → (0-4, 5) = (-4, 5)

THEN FINALLY

Translating point 4 units down will translate the coordinates from (-4, 5) to :

(x, y) → (x, y-4)

(-4, 5) → (-4, 5-4) = (-4, 1)

Therefore, the coordinates of point P(0, 0) after translating point 5 units up, then 4 units left, then 4 units down will be:

(x, y) → (x, y+5) → (x-4, y+5) → (x-4, y+5-4)

(0, 0) → (0, 0+5) → (0-4, 0+5) → (0-4, 0+5-4) = (-4, 1)

Hence, the coordinates of point P after all the translations become: (-4, 1)