(Solved): Consider the triangular region in the plane given by the triangle (1,4),(4,-2), and (-1,-4). HINT: U ...

Consider the triangular region in the plane given by the triangle

, and

. HINT: Use Desmos as a guide help to find the solutions. a. The horizontal line

intersects this region. What are the coordinates of the two boundary points it intersects? What is the length of the horizontal segment within the region along this line? b. What is the length of the section of the line

that lies within this region? c. If a robot starts at

and moves horizontally left at a constant speed of 0.55 units per second, when will it hit the lower boundary of the triangular region? d. If the robot starts at

and moves horizontally left at a constant speed of 0.75 units per second, when will it hit the left boundary of the triangular region? If the line segment connecting point

to point

is rotated

counterclockwise about point

(draw the new graph on the given coordinate plane): What is the slope of the original segment,

? What is the slope of the rotated segment? Explain and/or show how you know. Where does point

land? Now, rotate the original line

clockwise about point

(draw the new graph on the given coordinate plane): 4. What is the slope of the new rotated segment? Explain and/or show how you know. 5. Where does point

land?