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.

The rule of translation is .

The translated vector is .

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:

(Eq. 1)

Where:

- Original vector, dimensionless.

- Translation vector, dimensionless.

- Translated vector, dimensionless.

If we know that , then the rule of translation is described by:

(Eq. 2)

If , then the new location of A is:

The translated vector is .

x = 23.78

step-by-step explanation:

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh