Triangle \triangle ABC△ABCtriangle, A, B, C is reflected across line \ellℓell to create \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime.
What is the area of \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime?
Answers
Answer:
Triangle \triangle ABC△ABCtriangle, A, B, C is reflected across line L to create \triangle A'B'C'△A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime. What is the area of \triangle A'B'C'△A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime?
Step-by-step explanation:
The area of = The area of
Step-by-step explanation:
Given
Reflected to:
Required
Determine the area of
When a shape is reflected across any point to create another shape.
The newly created shape has the same area as the area of the reflected shape.
This is so because, reflection does not affect the dimension of shapes.
Having said that:
The area of = The area of
Answer:
6
Step-by-step explanation:
△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is a reflection of \triangle ABC△ABCtriangle, A, B, C. Reflections preserve segment lengths.
Segment \overline{CA}
CA
start overline, C, A, end overline corresponds to segment \overline{C'A'}
C
′
A
′
start overline, C, prime, A, prime, end overline, so CA=C'A'=3CA=C
′
A
′
=3C, A, equals, C, prime, A, prime, equals, 3 units. With this information, we are ready to calculate the area.
Hint #22 / 3
Let's calculate the area of the triangle.
\begin{aligned} \text{area}&=\dfrac{bh}{2} \\\\ &=\dfrac{3(4)}{2} \\\\ &=6 \end{aligned}
area
=
2
bh
=
2
3(4)
=6
Hint #33 / 3
In conclusion, the area of \triangle A'B'C'=6△A
′
B
′
C
′
=6triangle, A, prime, B, prime, C, prime, equals, 6 square units.