Mathematics
Δ ABC is reflected in origin to get Δ A'B'C'.
Statement 1: Δ ABC is congruent to Δ A'B'C'.
Statement 2: The two triangles are similar to each other.
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Reflection
1 Like
Answer
When a point (x, y) is reflected across the origin, its image becomes (-x, -y).
So, under this transformation:
All angles and side lengths are preserved.
The orientation (clockwise/counter-clockwise) is reversed, but the size and shape remain identical.
According to statement 1 : Δ ABC is congruent to Δ A'B'C' because in reflection lengths and angles are preserved.
So, statement 1 is true.
According to statement 2 : Δ ABC is similar to Δ A'B'C' because all congruent triangles are similar.
So, statement 2 is true.
Hence, option 1 is the correct option.
Answered By
1 Like
Related Questions
A triangle ABC is reflected in y-axis to get triangle A'B'C'. Triangle A'B'C' is reflected in line y = 0, to get △A"B"C". Then which of the following is not true ?
△A'B'C' ~ △A"B"C"
△A'B'C' ≅ △A"B"C"
△ABC ≅ △A"B"C"
△ABC ≠ △A"B"C"
Point M(x, y) is reflected in line AB, the reflection of M(x, y) in AB is the point M itself.
Assertion (A) : The reflection is called invariant transformation.
Reason (R) : In case of invariant transformation, the point is its own image.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for R.
Both A and R are true and R is incorrect reason for R.
Points (-5, 1) and (4, 1) are invariant points under reflection in the line L.
Statement 1: The equation of the line L is x = 1.
Statement 2: A point P is called an invariant point with respect to a given line L, if its image in the line L is the point P itself.
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Point A (4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.