The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph: part a: is the graph linear or nonlinear? explain your answer. (2 points) part b: in which segments is the graph increasing, decreasing, and constant? (3 points) part c: in your own words, describe the motion of the ant, as shown on the graph. (5 points)

A.  Non linear

B  The graph is increasing over the region from 0 to 2.  The graph is decreasing from 4 to 6. The graph is constant from 2 to 4.  

C. The ant leaves his hole at 0 seconds and starts walking away from the hole until 2 seconds.  He stops and waits until 4 seconds.  He then starts walking back to his hole at the same speed  until 6 seconds  when he is at his hole.

Step-by-step explanation:

Part A:  Is this graph linear or non linear?

A linear graph is a straight line.  This graph is piecewise linear, but is not a straight line over the entire region.  Therefore this graph is not linear.

Part B:  

The graph is increasing over the region from 0 to 2.  The slope is increasing during that time.  The graph is decreasing from 4 to 6.  The slope is decreasing during that time.  The graph is constant from 2 to 4.  The slope is 0 during that time.

Part C

The ant leaves his hole at 0 seconds and starts walking away from the hole until 2 seconds.  He stops and waits until 4 seconds.  He then starts walking back to his hole at the same speed  until 6 seconds  when he is at his hole.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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step-by-step explanation: