1) If point T was located at (4, 6) and was moved –3 in the x-direction and –2 in the y-direction, at what coordinates will point T be located?
- x-coordinate = 4
- y-coordinate = 6
If you want to move -3 in the x-direction and -2 in y-direction, you'll need to subtract -3 from 4 (i.e., x-coordinate) and -2 from 6 (i.e., y-coordinate).
ㅤㅤㅤ = T'(4 – 3, 6 – 2)
ㅤㅤㅤ = T'(1, 4)
2) Translate point G located at (–4, 0) +5 in the x-direction and +3 in the y-direction.
Here also, you'll need to follow the same procedure followed in the first question.
- x-coordinate = –4
- y-coordinate = 0 [tex]\:[/tex]
Translation: +5 in x-direction and +3 in y-direction.
Add 5 to the x-coordinate and 3 to the y-coordinate.
ㅤㅤㅤ = G'(–4 + 5, 0 + 3)
ㅤㅤㅤ = G'(1, 3)
3) A point was located at (–3, –2) and was located at (4, 5) after it was translated. How many units was it translated in the x-direction and the y-direction?
First position of the point: (–3, –2)
- x-coordinate = –3
- y-coordinate = –2
Second position of the point: (4, 5)
- x-coordinate = 4
- y-coordinate = 5
In order to find how many units were translated in the x-direction and y-direction, you'll need to subtract the x and y coordinates of its first position from its second position.
x-direction:
ㅤㅤㅤ = 4 – (–3)
ㅤㅤㅤ = 4 + 3
ㅤㅤㅤ = 7 units
y-direction:
ㅤㅤㅤ = 5 – (–2)
ㅤㅤㅤ = 5 + 2
ㅤㅤㅤ = 7 units
4) If a point was located at (–4, 5), how many units would it have to be translated in the x and y direction for the point to reach the origin.
- x-coordinate = –4
- y-coordinate = 5
If you want to find how many units should be translated from the given point in the x and y direction to reach the origin, you'll need to subtract the x and y coordinates from 0.
x-direction:
ㅤㅤㅤ = 0 – (–4)
ㅤㅤㅤ = 0 + 4
ㅤㅤㅤ = 4 units
y-direction:
ㅤㅤㅤ = 0 – 5
ㅤㅤㅤ = –5 units
