Question

Which statement is true about the slopes of BC and BE?

a) The slope of BC is the same as the slope of BE because ABC is similar to ADBE.
b) The slope of BE is 3 times the slope of BC because each side of ADBE is 3 times as long as each side of ABC.
c) The slope of BE is 9 times the slope of BC because the area of ADBE is 9 times the area of ABC.
d) The slope of BE is 8 more than the slope of BC because the legs of ADBE are 8 units longer than the legs of ABC.

Answer 1

The slope of BE is 3 times the slope of BC because each side of ADBE is 3 times as long as each side of ABC.

Step-by-step explanation:

The correct answer is b) The slope of BE is 3 times the slope of BC because each side of ADBE is 3 times as long as each side of ABC.

In similar triangles, the ratios of corresponding sides are equal. Since ADBE is similar to ABC, the ratio of the length of AB to BE is the same as the ratio of BC to AC. Since each side of ADBE is 3 times as long as each side of ABC, the ratio of BC to AC is 1:3. Therefore, the slope of BC is 1 and the slope of BE is 3.

So, the slope of BE is 3 times the slope of BC.