Question
What is the pre-image of the points (12, 7) if it has moved 4 units to the right and 3 units up?
- (8, 4)
- (4, 3)
- (4, 7)
- (3, 3)
Hint:
Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.
We have to find the pre-image of the points (12, 7) if it has moved 4 units to the right and 3 units up.
The correct answer is: (8, 4)
Now as we said that in translation, a point or a figure can move up, down, right, left, or anywhere else in the coordinate system. Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be displayed as an ordered pair (x, y) known as Coordinates.
We have to find the pre-image of (12,7) so we have to shift 4 units to the left and 3 units to down.
Lets consider x, we have to shift 4 units to left. So it will be:
x ---- 12-4
x --- 8
We have subtracted 4 because it is shifted to left side as we are finding pre-image.
Let's consider y, we have to shift 3 units to down. So it will be:
y ---- 7-3
y ---- 4
We have subtracted 3 because it is shifted on the lower side as we are finding pre-image.
So the algebraic representation will be: (12,7) → (8,4).
In this question, we used the concept of translation and found out the points according to the condition given. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. So the algebraic representation will be: (12,7) → (8,4).
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