Question

△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¯¯¯¯¯ .

Answer 1

Option B.

Explanation:

Slope of the line AC =
`\frac{\text{Rise}}{\text{Run}}`

=
`\frac{\text{AB}}{\text{BC}}`

=
`(4)/(6)`

=
`(2)/(3)`

Slope of the line CE =
`\frac{\text{DC}}{\text{DE}}`

=
`(2)/(3)`

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.