Translate the point (1, 3) to the new origin given ( h , k ). given center ( h , k ) = (5, 4), find point ( x ', y ').

(6,7)

Step-by-step explanation:

To translate a point, move each coordinate the specified amount and direction. Since the origin (0,0) moved to (5,4) or 5 right and 4 up, move (1,3) the same amount and direction. 1 moves right to 6. 3 moves up to 7. The new point is (6,7)

(-4,-1)

Step-by-step explanation:

(h,k)=(5,4) and (x,y)=(1,3)

x' = x - h = 1 - 5 = - 4

y' = y -k = 3 - 4 = - 1

3/6   and 9/18

step-by-step explanation:

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).