Question

Point A is located at (4, 7). It will be translated 5 units right and 3 units down. Write the rule and give the location of point A.

Answer 1

Answer:

The rule of translation is $A(x',y') = A(x,y) + (5,-3)$.

The translated vector is $A(x',y') = (9, 4)$.

Step-by-step explanation:

Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.

We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:

$A(x',y') = A(x,y) + U(x,y)$ (Eq. 1)

Where:

$A(x,y)$ - Original vector, dimensionless.

$U(x,y)$ - Translation vector, dimensionless.

$A(x',y')$ - Translated vector, dimensionless.

If we know that $U(x, y) = (5, -3)$, then the rule of translation is described by:

$A(x',y') = A(x,y) + (5,-3)$ (Eq. 2)

If $A(x, y) = (4,7)$, then the new location of A is:

$A(x',y') = (4,7)+(5,-3)$

$A(x',y') = (9, 4)$

The translated vector is $A(x',y') = (9, 4)$.