Question

Triangle abc in quadrant one with side ab of length 2 units, triangle a prime b prime c prime in quadrant four triangle abc has been reflected over the x-axis to create triangle a′b′c′. which of the following statements is true?

a. b′c′ = 2
b. a′b′ = 2
c. bc = 2
d. ac = 2

Answer 1

The correct statement after reflecting triangle ABC over the x-axis is b (A'B' = 2), due to the properties of reflected figures, which maintain the dimensions of the original figure.

Step-by-step explanation:

The student asked which statement is true after reflecting triangle ABC over the x-axis to create triangle A'B'C' given that side AB has a length of 2 units and is in quadrant one, and the reflected triangle is in quadrant four. When a shape is reflected over the x-axis, the x-coordinates of the points remain the same, while the y-coordinates are negated. However, the lengths of sides remain unchanged.

Therefore, based on the information provided, if AB = 2 units before the reflection, then the length of the corresponding side A'B' after the reflection will also be 2 units, making option b (A'B' = 2) the correct choice. This is consistent with the properties of reflected figures on a coordinate plane which maintain the dimensions of the original figure.