Question

the following diagram shows a right triangle.

which of the following reflective symmetries apply to the triangle?

symmetry | applies to the figure?
reflective symmetry over the line \\(y = -x\\) | yes/no
reflective symmetry over the \\(x\\)-axis | yes/no

Explanation:

Identify the vertices of the triangle

$$ V_1 = (4, 6),\quad V_2 = (4, -4),\quad V_3 = (-7, -4) $$

Test reflective symmetry over the line \(y = -x\)

$$ (x, y) \to (-y, -x) $$

$$ V_1(4, 6) \to (-6, -4) otin \{V_1, V_2, V_3\} $$

$$ \text{Result: No} $$

Test reflective symmetry over the \(x\)-axis

$$ (x, y) \to (x, -y) $$

$$ V_1(4, 6) \to (4, -6) otin \{V_1, V_2, V_3\} $$

$$ \text{Result: No} $$

Answer:

Question 1

Reflective symmetry over the line \(y = -x\): No

Question 2

Reflective symmetry over the \(x\)-axis: No