What is the translation of the point to its image?
A (−1, 4)→ A' (3, 3)

We conclude that the formula to determine the translation of the point to its image will be:

Step-by-step explanation:

Given

In other words:

A (−1, 4) → A' (3, 3)

We need to determine the translation of the point to its image.

It is clear that the coordinates of the image A' (3, 3) of the original point A (−1, 4) can be determined by adding 4 units to the x-coordinate and subtracting 1 unit to the y-coordinate.

Thus, the translation of the point to its image will be:

A (x, y) → A' (x+4, y-1)

Verification

As A(-1, 4), so using the translation formula:

A (x, y) → A' (x+4, y-1)

A (-1, 4) → A' (-1+4, 4-1) = A' (3, 3)

Therefore, we conclude that the formula to determine the translation of the point to its image will be:

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).