Students are practicing their dance for the school play. they need to startin position 1 located at (3,5) then go to position 2 at (1,2) , to position 3 at (-1,-1) and finnaly to position 4. describe the translation between each position, and give the location of the 4th position .

Part a) The translation between each position is 2 units to the left and 3 units down

Part b) The location of position 4 is (-3,-4)

Step-by-step explanation:

we know that

step 1

Position 1 is located at (3,5) and then go to position 2 at (1,2)

so

The rule of the translation Position 1 to Position 2 is

(x,y)> (x-2,y-3)

that means> The translation is 2 units to the left and 3 units down

step 2

Position 2 is located at (1,2) and then go to position 3 at (-1,-1)

so

The rule of the translation Position 2 to Position 3 is

(x,y)> (x-2,y-3)

that means> The translation is 2 units to the left and 3 units down

step 3

Find the location of the 4th position

Applying the rule of the translation to position 3 at (-1,-1)

(x,y)> (x-2,y-3)

(-1,-1)> (-1-2,-1-3) > (-3,-4)

The position 4 is (-3,-4)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

a

step-by-step explanation: