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△ABC and △CDE similar right triangles. The coordinates of all the vertices are integers.

A: The relationship between the slope of AC¯¯¯¯¯ and the slope of CE¯¯¯¯¯ cannot be determined, because the triangles are congruent.

B:The slope of AC¯¯¯¯¯ is equal to the slope of CE¯¯¯¯¯ . This this because ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC¯¯¯¯¯ as for CE¯¯¯¯¯

C:The slope of AC¯¯¯¯¯ is greater than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .

D:The slope of AC¯¯¯¯¯ is less than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .

ABC and CDE similar right triangles The coordinates of all the vertices are integers A The relationship between the slope of AC and the slope of CE cannot be de class=

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Answer:

Option B.

Step-by-step explanation:

Slope of the line AC = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                                  = [tex]\frac{\text{AB}}{\text{BC}}[/tex]

                                  = [tex]\frac{4}{6}[/tex]

                                  = [tex]\frac{2}{3}[/tex]

Slope of the line CE = [tex]\frac{\text{DC}}{\text{DE}}[/tex]

                                  = [tex]\frac{2}{3}[/tex]

Therefore, slope of the line AC = Slope of the line AC

And this is because ratio of change in y-values of the endpoints to the change  in x-values of the endpoints is the same for AC as for CE.

Option B. is the answer.

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