R(3, 8) is dilated by a factor of 5, centered at (2, 10). Write the coordinates of R’.

The coordinates of R' are .

Step-by-step explanation:

According to Linear Algebra, dilation consist in expanding a given vector with  respect to one of its endpoints by a scalar. That is:

(Eq. 1)

Where:

- Original location with respect to origin, dimensionless.

- Point of reference with respect to origin, dimensionless.

- Dilation factor, dimensionless.

- Dilated point with respect to origin, dimensionless.

If we know that , and , then the dilated point is:

The coordinates of R' are .

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).