Answer: The correct options are
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.
Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.
The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).
And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).
<u>Option (A) Rotation 90°:</u>
We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.
So, rotation of 90° anticlockwise is a correct option.
<u>Option (B) Rotation 180°:</u>
If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.
So, rotation of 180° is NOT a correct option.
<u>Option (C) Rotation 270°:</u>
If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.
So, rotation of 270° clockwise is also a correct option.
<u>Option (D) (x, y) → (–y, x):</u>
We see that the co-ordinates of both the triangle follow the transformation
X(0, 0) ⇒ X'(0, 0)
Y(0, -2) ⇒ Y'(2, 0)
Z(-2, -2) ⇒ Z'(2, -2).
So, the transformation is (x, y) ⇒ (-y, x).
Therefore, the transformation (x, y) → (–y, x) is a correct option.
<u>Option (E) (x, y) → (y, -x):</u>
We see that the co-ordinates of both the triangle does NOT follow this transformation
For example, suppose this transformation is correct. Then, we have
Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.
Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.
Thus, the correct options are:
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Answer:
Step-by-step explanation:
By applying <em>Pythagoras theorem</em> we can find hypotenuse of a right angle triangle.
Side of right angle triangle (a) = 5√2 cm
Side of right angle triangle (b) = 5√2 cm
Hypotenuse² = a² × b²
Answer:
B. Inscribed equilateral triangle.
Step-by-step explanation:
An equilateral triangle is a type of triangle that has all sides to have the same length.
An inscribed figure or shape is one which has been constructed within the boundaries of another figure or shape.
In the given question, the markings is construction of an inscribed equilateral triangle. This procedure of the construction after completion, generate the triangle as shown in the construction attached to this answer.
