A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (-3,4), and (1, 4). The city planner wants to plant a tree at the orthocenter of the park. What are the coordinates of the tree?

step-by-step explanation:

the answer is a) y= 2 csc [0.5 (x+pi/2)]-1

step-by-step explanation:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus